Complex Systems and Network Science

Topic Information

Dear Colleagues,

Complex systems, together with network science, are a field of immense significance, due both to their foundational nature and also their wide interdisciplinary nature. Complex systems and networks are present anywhere and cover a huge variety of categories, such as systems biology, ecology, epidemiology, engineering, information systems, physiology, social and economic systems, statistical linguistics, urban systems, and many more. In this topic, we welcome state-of-the-art contributions that can show the power of complex systems and network science, both at theoretical and practical level. We also welcome contributions that marry diverse fields, and in this sense, hybrid contributions that combine techniques from different fields using complex systems and/or network science are also accepted. The following list of arguments is just a short subset of the wide range of subtopics that are included in this call:

• Adaptive networks
• Cliques and communities
• Complex network topologies
• Complex systems and AI
• Complex systems and data science
• Complex systems education
• Computational methods
• Connectivity and centrality
• Criticality
• Dynamic scaling
• Dynamical networks
• Dynamics of information
• Evolution, development, and adaptation
• Industrial applications of complex systems
• Motifs
• Multilayer and multiplex networks
• Multiscale structure and dynamics
• Network efficiency
• Network modeling and analysis
• Network visualization
• Nonlinear dynamics and chaos
• Pattern formation
• Robustness and resilience
• Self-similarity and fractals
• Self-organization
• Small-world and scale-free networks
• Spatiotemporal patterns
• Temporal correlations
• Temporal networks

We welcome contributions that can advance the field in various ways, including case studies, perspectives, research articles and reviews.

Prof. Dr. Massimo Marchiori
Prof. Dr. Latora Vito
Topic Editors

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Algorithms algorithms	1.8	4.1	2008	18.9 Days	CHF 1600
Entropy entropy	2.1	4.9	1999	22.3 Days	CHF 2600
Future Internet futureinternet	2.8	7.1	2009	16.9 Days	CHF 1600
Mathematics mathematics	2.3	4.0	2013	18.3 Days	CHF 2600
Symmetry symmetry	2.2	5.4	2009	17.3 Days	CHF 2400

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Published Papers (37 papers)

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All Algorithms Entropy Future Internet Mathematics Symmetry

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Open AccessArticle

Network Higher-Order Structure Dismantling

by Peng Peng, Tianlong Fan and Linyuan Lü

Entropy 2024, 26(3), 248; https://doi.org/10.3390/e26030248 - 11 Mar 2024

Cited by 5 | Viewed by 2335

Abstract

Diverse higher-order structures, foundational for supporting a network’s “meta-functions”, play a vital role in structure, functionality, and the emergence of complex dynamics. Nevertheless, the problem of dismantling them has been consistently overlooked. In this paper, we introduce the concept of dismantling higher-order structures, [...] Read more.

Diverse higher-order structures, foundational for supporting a network’s “meta-functions”, play a vital role in structure, functionality, and the emergence of complex dynamics. Nevertheless, the problem of dismantling them has been consistently overlooked. In this paper, we introduce the concept of dismantling higher-order structures, with the objective of disrupting not only network connectivity but also eradicating all higher-order structures in each branch, thereby ensuring thorough functional paralysis. Given the diversity and unknown specifics of higher-order structures, identifying and targeting them individually is not practical or even feasible. Fortunately, their close association with k-cores arises from their internal high connectivity. Thus, we transform higher-order structure measurement into measurements on k-cores with corresponding orders. Furthermore, we propose the Belief Propagation-guided Higher-order Dismantling (BPHD) algorithm, minimizing dismantling costs while achieving maximal disruption to connectivity and higher-order structures, ultimately converting the network into a forest. BPHD exhibits the explosive vulnerability of network higher-order structures, counterintuitively showcasing decreasing dismantling costs with increasing structural complexity. Our findings offer a novel approach for dismantling malignant networks, emphasizing the substantial challenges inherent in safeguarding against such malicious attacks. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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21 pages, 6720 KiB  

Open AccessArticle

Fuzzy-Based Active Queue Management Using Precise Fuzzy Modeling and Genetic Algorithm

by Ahmad Adel Abu-Shareha, Adeeb Alsaaidah, Ali Alshahrani and Basil Al-Kasasbeh

Symmetry 2023, 15(9), 1733; https://doi.org/10.3390/sym15091733 - 10 Sep 2023

Cited by 2 | Viewed by 1251

Abstract

Active Queue Management (AQM) methods significantly impact the network performance, as they manage the router queue and facilitate the traffic flow through the network. This paper presents a novel fuzzy-based AQM method developed with a computationally efficient precise fuzzy modeling optimized using the [...] Read more.

Active Queue Management (AQM) methods significantly impact the network performance, as they manage the router queue and facilitate the traffic flow through the network. This paper presents a novel fuzzy-based AQM method developed with a computationally efficient precise fuzzy modeling optimized using the Genetic Algorithm. The proposed method focuses on the concept of symmetry as a means to achieve a more balanced and equitable distribution of the resources and avoid bandwidth wasting resulting from unnecessary packet dropping. The proposed method calculates the dropping probability of each packet using a precise fuzzy model that was created and tuned in advance and based on the previous dropping probability value and the queue length. The tuning process is implemented as an optimization problem formulated for the b₀, b₁, and b₂ variables of the precise rules with an objective function that maximizes the performance results in terms of loss, dropping, and delay. To prove the efficiency of the developed method, the simulation was not limited to the common Bernoulli process simulation; instead, the Markov-modulated Bernoulli process was used to mimic the burstiness nature of the traffic. The simulation is conducted on a machine operated with 64-bit Windows 10 with an Intel Core i7 2.0 GHz processor and 16 GB of RAM. The simulation used Java programming language in Apache NetBeans Integrated Development Environment (IDE) 11.2. The results showed that the proposed method outperformed the existing methods in terms of computational complexity, packet loss, dropping, and delay. As such, in low congested networks, the proposed method maintained no packet loss and dropped 22% of the packets with an average delay of 7.57, compared to the best method, LRED, which dropped 21% of the packets with a delay of 10.74, and FCRED, which dropped 21% of the packets with a delay of 16.54. In highly congested networks, the proposed method also maintained no packet loss and dropped 48% of the packets, with an average delay of 16.23, compared to the best method LRED, which dropped 47% of the packets with a delay of 28.04, and FCRED, which dropped 46% of the packets with a delay of 40.23. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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22 pages, 4459 KiB  

Open AccessArticle

A Symmetrical Fuzzy Neural Network Regression Method Coordinating Structure and Parameter Identifications for Regression

by Ke Zhang, Wenning Hao, Xiaohan Yu and Tianhao Shao

Symmetry 2023, 15(9), 1711; https://doi.org/10.3390/sym15091711 - 6 Sep 2023

Cited by 1 | Viewed by 1761

Abstract

Fuzzy neural networks have both the interpretability of fuzzy systems and the self-learning ability of neural networks, but they will face the challenge of “rule explosion” when dealing with high-dimensional data. Moreover, the structure and parameter identifications of models are generally performed in [...] Read more.

Fuzzy neural networks have both the interpretability of fuzzy systems and the self-learning ability of neural networks, but they will face the challenge of “rule explosion” when dealing with high-dimensional data. Moreover, the structure and parameter identifications of models are generally performed in two stages, and this always attends to one thing and loses another in terms of interpretability and predictive performance. In this paper, a fuzzy neural network regression method (FNNR) that coordinates structure identification and parameter identification is proposed. To alleviate the problem of rule explosion, the structure identification and parameter identification are coordinated in the training process, and the numbers of fuzzy rules and fuzzy partitions are effectively limited, while the parameters of fuzzy rules are optimized. The symmetrical architecture of the FNNR is designed for automatic structure identification. An alternate training strategy is adopted by treating discrete and continuous parameters differently, and thus the convergence efficiency of the algorithm is improved. To enhance interpretability, regularized terms are designed from fuzzy rule level and fuzzy partition level to guide the model to learn fuzzy rules with simple structures and clear semantics. The experimental results show that the proposed method has both a compact structure and high precision. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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13 pages, 3333 KiB  

Open AccessArticle

Leveraging Minimum Nodes for Optimum Key Player Identification in Complex Networks: A Deep Reinforcement Learning Strategy with Structured Reward Shaping

by Li Zeng, Changjun Fan and Chao Chen

Mathematics 2023, 11(17), 3690; https://doi.org/10.3390/math11173690 - 28 Aug 2023

Cited by 2 | Viewed by 1979

Abstract

The problem of finding key players in a graph, also known as network dismantling, or network disintegration, aims to find an optimal removal sequence of nodes (edges, substructures) through a certain algorithm, ultimately causing functional indicators such as the largest connected component (GCC) [...] Read more.

The problem of finding key players in a graph, also known as network dismantling, or network disintegration, aims to find an optimal removal sequence of nodes (edges, substructures) through a certain algorithm, ultimately causing functional indicators such as the largest connected component (GCC) or network pair connectivity in the graph to rapidly decline. As a typical NP-hard problem on graphs, recent methods based on reinforcement learning and graph representation learning have effectively solved such problems. However, existing reinforcement-learning-based key-player-identification algorithms often need to remove too many nodes in order to achieve the optimal effect when removing the remaining network until no connected edges remain. The use of a minimum number of nodes while maintaining or surpassing the performance of existing methods is a worthwhile research problem. To this end, a novel algorithm called MiniKey was proposed to tackle such challenges, which employs a specific deep Q-network architecture for reinforcement learning, a novel reward-shaping mechanism based on network functional indicators, and the graph-embedding technique GraphSage to transform network nodes into latent representations. Additionally, a technique dubbed ‘virtual node technology’ is integrated to grasp the overarching feature representation of the whole network. This innovative algorithm can be effectively trained on small-scale simulated graphs while also being scalable to large-scale real-world networks. Importantly, experiments from both six simulated datasets and six real-world datasets demonstrates that MiniKey can achieve optimal performance, striking a perfect balance between the effectiveness of key node identification and the minimization of the number of nodes that is utilized, which holds potential for real-world applications such as curbing misinformation spread in social networks, optimizing traffic in transportation systems, and identifying key targets in biological networks for targeted interventions. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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17 pages, 4147 KiB  

Open AccessArticle

HLEGF: An Effective Hypernetwork Community Detection Algorithm Based on Local Expansion and Global Fusion

by Feng Wang, Feng Hu, Rumeng Chen and Naixue Xiong

Mathematics 2023, 11(16), 3497; https://doi.org/10.3390/math11163497 - 13 Aug 2023

Cited by 2 | Viewed by 1531

Abstract

Community structure is crucial for understanding network characteristics, and the local expansion method has performed well in detecting community structures. However, there are two problems with this method. Firstly, it can only add nodes or edges on the basis of existing clusters, and [...] Read more.

Community structure is crucial for understanding network characteristics, and the local expansion method has performed well in detecting community structures. However, there are two problems with this method. Firstly, it can only add nodes or edges on the basis of existing clusters, and secondly, it can produce a large number of small communities. In this paper, we extend the local expansion method based on ordinary graph to hypergraph, and propose an effective hypernetwork community detection algorithm based on local expansion (LE) and global fusion (GF), which is referred to as HLEGF. The LE process obtains multiple small sub-hypergraphs by deleting and adding hyperedges, while the GF process optimizes the sub-hypergraphs generated by the local expansion process. To solve the first problem, the HLEGF algorithm introduces the concepts of community neighborhood and community boundary to delete some nodes and hyperedges in hypergraphs. To solve the second problem, the HLEGF algorithm establishes correlations between adjacent sub-hypergraphs through global fusion. We evaluated the performance of the HLEGF algorithm in the real hypernetwork and six synthetic random hypernetworks with different probabilities. Because the HLEGF algorithm introduces the concepts of community boundary and neighborhood, and the concept of a series of similarities, the algorithm has superiority. In the real hypernetwork, the HLEGF algorithm is consistent with the classical Spectral algorithm, while in the random hypernetwork, when the probability is not less than 0.95, the NMI value of the HLEGF algorithm is always greater than 0.92, and the RI value is always greater than 0.97. When the probability is 0.95, the HLEGF algorithm achieves a 2.3% improvement in the NMI value, compared to the Spectral algorithm. Finally, we applied the HLEGF algorithm to the drug–target hypernetwork to partition drugs with similar functions into communities. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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19 pages, 1612 KiB  

Open AccessArticle

Distributed Consensus Algorithms in Sensor Networks with Higher-Order Topology

by Qianyi Chen, Wenyuan Shi, Dongyan Sui and Siyang Leng

Entropy 2023, 25(8), 1200; https://doi.org/10.3390/e25081200 - 11 Aug 2023

Cited by 3 | Viewed by 1535

Abstract

Information aggregation in distributed sensor networks has received significant attention from researchers in various disciplines. Distributed consensus algorithms are broadly developed to accelerate the convergence to consensus under different communication and/or energy limitations. Non-Bayesian social learning strategies are representative algorithms for distributed agents [...] Read more.

Information aggregation in distributed sensor networks has received significant attention from researchers in various disciplines. Distributed consensus algorithms are broadly developed to accelerate the convergence to consensus under different communication and/or energy limitations. Non-Bayesian social learning strategies are representative algorithms for distributed agents to learn progressively an underlying state of nature by information communications and evolutions. This work designs a new non-Bayesian social learning strategy named the hypergraph social learning by introducing the higher-order topology as the underlying communication network structure, with its convergence as well as the convergence rate theoretically analyzed. Extensive numerical examples are provided to demonstrate the effectiveness of the framework and reveal its superior performance when applying to sensor networks in tasks such as cooperative positioning. The designed framework can assist sensor network designers to develop more efficient communication topology, which can better resist environmental obstructions, and also has theoretical and applied values in broad areas such as distributed parameter estimation, dispersed information aggregation and social networks. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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19 pages, 5286 KiB  

Open AccessArticle

Identifying Key Factors of Hazardous Materials Transportation Accidents Based on Higher-Order and Multilayer Networks

by Cuiping Ren, Bianbian Chen and Fengjie Xie

Entropy 2023, 25(7), 1036; https://doi.org/10.3390/e25071036 - 10 Jul 2023

Cited by 4 | Viewed by 2140

Abstract

This paper focuses on the application of higher-order and multilayer networks in identifying critical causes and relationships contributing to hazardous materials transportation accidents. There were 792 accidents of hazardous materials transportation that occurred on the road from 2017 to 2021 which have been [...] Read more.

This paper focuses on the application of higher-order and multilayer networks in identifying critical causes and relationships contributing to hazardous materials transportation accidents. There were 792 accidents of hazardous materials transportation that occurred on the road from 2017 to 2021 which have been investigated. By considering time sequence and dependency of causes, the hazardous materials transportation accidents causation network (HMTACN) was described using the higher-order model. To investigate the structure of HMTACN such as the importance of causes and links, HMTACN was divided into three layers using the weighted k-core decomposition: the core layer, the bridge layer and the peripheral layer. Then causes and links were analyzed in detail. It was found that the core layer was tightly connected and supported most of the causal flows of HMTACN. The results showed that causes should be given hierarchical attention. This study provides an innovative method to analyze complicated accidents, which can be used in identifying major causes and links. And this paper brings new ideas about safety network study and extends the applications of complex network theory. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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12 pages, 1043 KiB  

Open AccessArticle

Influence of Removing Leaf Node Neighbors on Network Controllability

by Chengpei Wu, Siyi Xu, Zhuoran Yu and Junli Li

Entropy 2023, 25(6), 945; https://doi.org/10.3390/e25060945 - 15 Jun 2023

Cited by 1 | Viewed by 1971

Abstract

From the perspective of network attackers, finding attack sequences that can cause significant damage to network controllability is an important task, which also helps defenders improve robustness during network constructions. Therefore, developing effective attack strategies is a key aspect of research on network [...] Read more.

From the perspective of network attackers, finding attack sequences that can cause significant damage to network controllability is an important task, which also helps defenders improve robustness during network constructions. Therefore, developing effective attack strategies is a key aspect of research on network controllability and its robustness. In this paper, we propose a Leaf Node Neighbor-based Attack (LNNA) strategy that can effectively disrupt the controllability of undirected networks. The LNNA strategy targets the neighbors of leaf nodes, and when there are no leaf nodes in the network, the strategy attacks the neighbors of nodes with a higher degree to produce the leaf nodes. Results from simulations on synthetic and real-world networks demonstrate the effectiveness of the proposed method. In particular, our findings suggest that removing neighbors of low-degree nodes (i.e., nodes with degree 1 or 2) can significantly reduce the controllability robustness of networks. Thus, protecting such low-degree nodes and their neighbors during network construction can lead to networks with improved controllability robustness. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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12 pages, 6428 KiB  

Open AccessArticle

Evolutionary Method of Heterogeneous Combat Network Based on Link Prediction

by Shaoming Qiu, Fen Chen, Yahui Wang and Jiancheng Zhao

Entropy 2023, 25(5), 812; https://doi.org/10.3390/e25050812 - 17 May 2023

Viewed by 1610

Abstract

Currently, research on the evolution of heterogeneous combat networks (HCNs) mainly focuses on the modeling process, with little attention paid to the impact of changes in network topology on operational capabilities. Link prediction can provide a fair and unified comparison standard for network [...] Read more.

Currently, research on the evolution of heterogeneous combat networks (HCNs) mainly focuses on the modeling process, with little attention paid to the impact of changes in network topology on operational capabilities. Link prediction can provide a fair and unified comparison standard for network evolution mechanisms. This paper uses link prediction methods to study the evolution of HCNs. Firstly, according to the characteristics of HCNs, a link prediction index based on frequent subgraphs (LPFS) is proposed. LPFS have been demonstrated on a real combat network to be superior to 26 baseline methods. The main driving force of research on evolution is to improve the operational capabilities of combat networks. Adding the same number of nodes and edges, 100 iterative experiments demonstrate that the evolutionary method (HCNE) proposed in this paper outperforms random evolution and preferential evolution in improving the operational capabilities of combat networks. Furthermore, the new network generated after evolution is more consistent with the characteristics of a real network. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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17 pages, 2950 KiB  

Open AccessArticle

An Influence-Based Label Propagation Algorithm for Overlapping Community Detection

by Hao Xu, Yuan Ran, Junqian Xing and Li Tao

Mathematics 2023, 11(9), 2133; https://doi.org/10.3390/math11092133 - 2 May 2023

Cited by 5 | Viewed by 2721

Abstract

Of the various characteristics of network structure, the community structure has received the most research attention. In social networks, communities are divided into overlapping communities and disjoint communities. The former are closer to the actual situation of real society than the latter, making [...] Read more.

Of the various characteristics of network structure, the community structure has received the most research attention. In social networks, communities are divided into overlapping communities and disjoint communities. The former are closer to the actual situation of real society than the latter, making it necessary to explore a more effective overlapping community detection algorithm. The label propagation algorithm (LPA) has been widely used in large-scale data owing to its low time cost. In the traditional LPA, all of the nodes are regarded as equivalent relationships. In this case, unreliable nodes reduce the accuracy of label propagation. To solve this problem, we propose the influence-based community overlap propagation algorithm (INF-COPRA) for ranking the influence of nodes and labels. To control the propagation process and prevent error propagation, the algorithm only provides influential nodes with labels in the initialization phase, and those labels with high influence are preferred in the propagation process. Lastly, the accuracy of INF-COPRA and existing algorithms is compared on benchmark networks and real networks. The experimental results show that the INF-COPRA algorithm significantly improves the extentded modularity (EQ) and normal mutual information (NMI) of the community, indicating that it can outperform state-of-art methods in overlapping community detection tasks. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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22 pages, 2449 KiB  

Open AccessArticle

Stirling Numbers of Uniform Trees and Related Computational Experiments

by Amir Barghi and Daryl DeFord

Algorithms 2023, 16(5), 223; https://doi.org/10.3390/a16050223 - 27 Apr 2023

Cited by 2 | Viewed by 1704

Abstract

The Stirling numbers for graphs provide a combinatorial interpretation of the number of cycle covers in a given graph. The problem of generating all cycle covers or enumerating these quantities on general graphs is computationally intractable, but recent work has shown that there [...] Read more.

The Stirling numbers for graphs provide a combinatorial interpretation of the number of cycle covers in a given graph. The problem of generating all cycle covers or enumerating these quantities on general graphs is computationally intractable, but recent work has shown that there exist infinite families of sparse or structured graphs for which it is possible to derive efficient enumerative formulas. In this paper, we consider the case of trees and forests of a fixed size, proposing an efficient algorithm based on matrix algebra to approximate the distribution of Stirling numbers. We also present a model application of machine learning to enumeration problems in this setting, demonstrating that standard regression techniques can be applied to this type of combinatorial structure. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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13 pages, 1015 KiB  

Open AccessArticle

SpreadRank: A Novel Approach for Identifying Influential Spreaders in Complex Networks

by Xuejin Zhu and Jie Huang

Entropy 2023, 25(4), 637; https://doi.org/10.3390/e25040637 - 10 Apr 2023

Cited by 7 | Viewed by 2137

Abstract

Identifying influential spreaders in complex networks is critical for information spread and malware diffusion suppression. In this paper, we propose a novel influential spreader identification method, called SpreadRank, which considers the path reachability in information spreading and uses its quantitative index as a [...] Read more.

Identifying influential spreaders in complex networks is critical for information spread and malware diffusion suppression. In this paper, we propose a novel influential spreader identification method, called SpreadRank, which considers the path reachability in information spreading and uses its quantitative index as a measure of node spread centrality to obtain the spread influence of a single node. To avoid the overlapping of the influence range of the node spread, this method establishes a dynamic influential node set selection mechanism based on the spread centrality value and the principle of minimizing the maximum connected branch after network segmentation, and it selects a group of nodes with the greatest overall spread influence. Experiments based on the SIR model demonstrate that, compared to other existing methods, the selected influential spreaders of SpreadRank can quickly diffuse or suppress information more effectively. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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13 pages, 690 KiB  

Open AccessArticle

Estimating the Number of Communities in Weighted Networks

by Huan Qing

Entropy 2023, 25(4), 551; https://doi.org/10.3390/e25040551 - 23 Mar 2023

Cited by 2 | Viewed by 1798

Abstract

Community detection in weighted networks has been a popular topic in recent years. However, while there exist several flexible methods for estimating communities in weighted networks, these methods usually assume that the number of communities is known. It is usually unclear how to [...] Read more.

Community detection in weighted networks has been a popular topic in recent years. However, while there exist several flexible methods for estimating communities in weighted networks, these methods usually assume that the number of communities is known. It is usually unclear how to determine the exact number of communities one should use. Here, to estimate the number of communities for weighted networks generated from arbitrary distribution under the degree-corrected distribution-free model, we propose one approach that combines weighted modularity with spectral clustering. This approach allows a weighted network to have negative edge weights and it also works for signed networks. We compare the proposed method to several existing methods and show that our method is more accurate for estimating the number of communities both numerically and empirically. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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15 pages, 2173 KiB  

Open AccessArticle

Event-Triggered Control for Intra/Inter-Layer Synchronization and Quasi-Synchronization in Two-Layer Coupled Networks

by Cheng Zhang, Chuan Zhang, Fanwei Meng and Yi Liang

Mathematics 2023, 11(6), 1458; https://doi.org/10.3390/math11061458 - 17 Mar 2023

Cited by 7 | Viewed by 1822

Abstract

This paper studies the intra/inter-layer synchronization and quasi-synchronization in two-layer coupled networks via event-triggered control, in which different layers have mutually independent topologies. First, based on Lyapunov stability theory and event-triggered thoughts, hybrid controllers are designed, respectively, for intra-layer synchronization (ALS) and inter-layer [...] Read more.

This paper studies the intra/inter-layer synchronization and quasi-synchronization in two-layer coupled networks via event-triggered control, in which different layers have mutually independent topologies. First, based on Lyapunov stability theory and event-triggered thoughts, hybrid controllers are designed, respectively, for intra-layer synchronization (ALS) and inter-layer synchronization (RLS). Second, a novel event-triggered rule is proposed, under which intra-layer quasi-synchronization (ALQS) and inter-layer quasi-synchronization (RLQS) can be respectively realized, and the event-triggered frequency can be greatly reduced. Moreover, the upper bound of the synchronization error can be flexibly adjusted by changing the parameters in event-triggered conditions, and the Zeno phenomenon about event-triggered control is also discussed in this paper. Finally, numerical examples are provided to confirm the correctness and validity of the proposed scheme. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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18 pages, 5775 KiB  

Open AccessArticle

An Analysis of Actors in Malay Films: Small Worlds, Centralities and Genre Diversity

by Nurun Najwa Bahari, Paul Expert and Fatimah Abdul Razak

Mathematics 2023, 11(5), 1252; https://doi.org/10.3390/math11051252 - 4 Mar 2023

Cited by 3 | Viewed by 4700

Abstract

This article utilizes social network analysis in addition to a measure of genre diversity to quantify the quality and capacity of actors in the Malay language film industry. We built a dataset by collecting data from various websites pertaining to Malay films. The [...] Read more.

This article utilizes social network analysis in addition to a measure of genre diversity to quantify the quality and capacity of actors in the Malay language film industry. We built a dataset by collecting data from various websites pertaining to Malay films. The data consists of 180 Malay films released from 2015 until 2020. The actor network is then built by connecting actors co-starring in a movie together and is compared to small world networks. We quantified the quality of actors in the network using five measures: number of films (TFA), degree centrality (DC), strength centrality (SC), betweenness centrality (BC), and normalized Herfindahl–Hirschman Index (NHHI). TFA, DC and SC indicate experience in the industry, since a high TFA shows that an actor has acted in more films. A high DC shows an actor has worked with many co-stars, and a high SC reflects an actor’s frequency of co-occurrence relationship. Actors with high TFA, DC, and SC are popular in this sense. Meanwhile, BC highlights the social importance of an actor in the network where they are the middlemen that connect actors from different genres of movies in the network, and we found that high BC actors are voice actors that may not have a high TFA, DC, or SC. NHHI highlights the actor’s capability to work with different types of film, and it serves as an important measure of an actor’s versatility. Moreover, we also calculated the average shortest path in the network to search for the “Kevin Bacon” of the Malay language film actor network. Using NHHI as an indicator of genre diversity, we also show that most of the actors diversify their work over the years and that genre diversity is an important benchmark for an actor. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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18 pages, 3458 KiB  

Open AccessArticle

Multi-Agent Deep Q-Network Based Dynamic Controller Placement for Node Variable Software-Defined Mobile Edge-Cloud Computing Networks

by Chenglin Xu, Cheng Xu and Bo Li

Mathematics 2023, 11(5), 1247; https://doi.org/10.3390/math11051247 - 4 Mar 2023

Cited by 3 | Viewed by 1795

Abstract

Software-defined networks (SDN) can use the control plane to manage heterogeneous devices efficiently, improve network resource utilization, and optimize Mobile Edge-Cloud Computing Networks (MECCN) network performance through decisions based on global information. However, network traffic in MECCNs can change over time and affect [...] Read more.

Software-defined networks (SDN) can use the control plane to manage heterogeneous devices efficiently, improve network resource utilization, and optimize Mobile Edge-Cloud Computing Networks (MECCN) network performance through decisions based on global information. However, network traffic in MECCNs can change over time and affect the performance of the SDN control plane. Moreover, the MECCN network may need to temporarily add network access points when the network load is excessive, and it is difficult for the control plane to form effective management of temporary nodes. This paper investigates the dynamic controller placement problem (CPP) in SDN-enabled Mobile Edge-Cloud Computing Networks (SD-MECCN) to enable the control plane to continuously and efficiently serve the network under changing network load and network access points. We consider the deployment of a two-layer structure with a control plane and construct the CPP based on this control plane. Subsequently, we solve this problem based on multi-agent DQN (MADQN), in which multiple agents cooperate to solve CPP and adjust the number of controllers according to the network load. The experimental results show that the proposed dynamic controller deployment algorithm based on MADQN for node-variable networks in this paper can achieve better performance in terms of delay, load difference, and control reliability than the Louvain-based algorithm, single-agent DQN-based algorithm, and MADQN- (without node-variable networks consideration) based algorithm. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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19 pages, 1155 KiB  

Open AccessEditor’s ChoiceArticle

Random Walks on Networks with Centrality-Based Stochastic Resetting

by Kiril Zelenkovski, Trifce Sandev, Ralf Metzler, Ljupco Kocarev and Lasko Basnarkov

Entropy 2023, 25(2), 293; https://doi.org/10.3390/e25020293 - 4 Feb 2023

Cited by 12 | Viewed by 2762

Abstract

We introduce a refined way to diffusely explore complex networks with stochastic resetting where the resetting site is derived from node centrality measures. This approach differs from previous ones, since it not only allows the random walker with a certain probability to jump [...] Read more.

We introduce a refined way to diffusely explore complex networks with stochastic resetting where the resetting site is derived from node centrality measures. This approach differs from previous ones, since it not only allows the random walker with a certain probability to jump from the current node to a deliberately chosen resetting node, rather it enables the walker to jump to the node that can reach all other nodes faster. Following this strategy, we consider the resetting site to be the geometric center, the node that minimizes the average travel time to all the other nodes. Using the established Markov chain theory, we calculate the Global Mean First Passage Time (GMFPT) to determine the search performance of the random walk with resetting for different resetting node candidates individually. Furthermore, we compare which nodes are better resetting node sites by comparing the GMFPT for each node. We study this approach for different topologies of generic and real-life networks. We show that, for directed networks extracted for real-life relationships, this centrality focused resetting can improve the search to a greater extent than for the generated undirected networks. This resetting to the center advocated here can minimize the average travel time to all other nodes in real networks as well. We also present a relationship between the longest shortest path (the diameter), the average node degree and the GMFPT when the starting node is the center. We show that, for undirected scale-free networks, stochastic resetting is effective only for networks that are extremely sparse with tree-like structures as they have larger diameters and smaller average node degrees. For directed networks, the resetting is beneficial even for networks that have loops. The numerical results are confirmed by analytic solutions. Our study demonstrates that the proposed random walk approach with resetting based on centrality measures reduces the memoryless search time for targets in the examined network topologies. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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19 pages, 733 KiB  

Open AccessArticle

Pairing Optimization via Statistics: Algebraic Structure in Pairing Problems and Its Application to Performance Enhancement

by Naoki Fujita, André Röhm, Takatomo Mihana, Ryoichi Horisaki, Aohan Li, Mikio Hasegawa and Makoto Naruse

Entropy 2023, 25(1), 146; https://doi.org/10.3390/e25010146 - 11 Jan 2023

Viewed by 2052

Abstract

Fully pairing all elements of a set while attempting to maximize the total benefit is a combinatorically difficult problem. Such pairing problems naturally appear in various situations in science, technology, economics, and other fields. In our previous study, we proposed an efficient method [...] Read more.

Fully pairing all elements of a set while attempting to maximize the total benefit is a combinatorically difficult problem. Such pairing problems naturally appear in various situations in science, technology, economics, and other fields. In our previous study, we proposed an efficient method to infer the underlying compatibilities among the entities, under the constraint that only the total compatibility is observable. Furthermore, by transforming the pairing problem into a traveling salesman problem with a multi-layer architecture, a pairing optimization algorithm was successfully demonstrated to derive a high-total-compatibility pairing. However, there is substantial room for further performance enhancement by further exploiting the underlying mathematical properties. In this study, we prove the existence of algebraic structures in the pairing problem. We transform the initially estimated compatibility information into an equivalent form where the variance of the individual compatibilities is minimized. We then demonstrate that the total compatibility obtained when using the heuristic pairing algorithm on the transformed problem is significantly higher compared to the previous method. With this improved perspective on the pairing problem using fundamental mathematical properties, we can contribute to practical applications such as wireless communications beyond 5G, where efficient pairing is of critical importance. As the pairing problem is a special case of the maximum weighted matching problem, our findings may also have implications for other algorithms on fully connected graphs. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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15 pages, 3452 KiB  

Open AccessArticle

Attack–Defense Game Model with Multi-Type Attackers Considering Information Dilemma

by Gaoxin Qi, Jichao Li, Chi Xu, Gang Chen and Kewei Yang

Entropy 2023, 25(1), 57; https://doi.org/10.3390/e25010057 - 28 Dec 2022

Cited by 10 | Viewed by 2368

Abstract

Today, people rely heavily on infrastructure networks. Attacks on infrastructure networks can lead to significant property damage and production stagnation. The game theory provides a suitable theoretical framework for solving the problem of infrastructure protection. Existing models consider only the beneficial effects that [...] Read more.

Today, people rely heavily on infrastructure networks. Attacks on infrastructure networks can lead to significant property damage and production stagnation. The game theory provides a suitable theoretical framework for solving the problem of infrastructure protection. Existing models consider only the beneficial effects that the defender obtains from information gaps. If the attacker’s countermeasures are ignored, the defender will become passive. Herein, we consider that a proficient attacker with a probability in the game can fill information gaps in the network. First, we introduce the link-hiding rule and the information dilemma. Second, based on the Bayesian static game model, we establish an attack–defense game model with multiple types of attackers. In the game model, we consider resource-consistent and different types of distributions of the attacker. Then, we introduce the solution method of our model by combining the Harsanyi transformation and the bi-matrix game. Finally, we conduct experiments using a scale-free network. The result shows that the defender can be benefited by hiding some links when facing a normal attacker or by estimating the distribution of the attacker correctly. The defender will experience a loss if it ignores the proficient attacker or misestimates the distribution. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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18 pages, 4580 KiB  

Open AccessArticle

Robustness of Cloud Manufacturing System Based on Complex Network and Multi-Agent Simulation

by Xin Zheng and Xiaodong Zhang

Entropy 2023, 25(1), 45; https://doi.org/10.3390/e25010045 - 27 Dec 2022

Cited by 3 | Viewed by 1910

Abstract

Cloud manufacturing systems (CMSs) are networked, distributed and loosely coupled, so they face great uncertainty and risk. This paper combines the complex network model with multi-agent simulation in a novel approach to the robustness analysis of CMSs. Different evaluation metrics are chosen for [...] Read more.

Cloud manufacturing systems (CMSs) are networked, distributed and loosely coupled, so they face great uncertainty and risk. This paper combines the complex network model with multi-agent simulation in a novel approach to the robustness analysis of CMSs. Different evaluation metrics are chosen for the two models, and three different robustness attack strategies are proposed. To verify the effectiveness of the proposed method, a case study is then conducted on a cloud manufacturing project of a new energy vehicle. The results show that both the structural and process-based robustness of the system are lowest under the betweenness-based failure mode, indicating that resource nodes with large betweenness are most important to the robustness of the project. Therefore, the cloud manufacturing platform should focus on monitoring and managing these resources so that they can provide stable services. Under the individual server failure mode, system robustness varies greatly depending on the failure behavior of the service provider: Among the five service providers (S1–S5) given in the experimental group, the failure of Server 1 leads to a sharp decline in robustness, while the failure of Server 2 has little impact. This indicates that the CMS can protect its robustness by identifying key servers and strengthening its supervision of them to prevent them from exiting the platform. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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8 pages, 2591 KiB  

Open AccessArticle

Critical Percolation on Temporal High-Speed Railway Networks

by Yi Liu, Senbin Yu, Chaoyang Zhang, Peiran Zhang, Yang Wang and Liang Gao

Mathematics 2022, 10(24), 4695; https://doi.org/10.3390/math10244695 - 11 Dec 2022

Cited by 2 | Viewed by 1685

Abstract

Deeply understanding the dynamic operating characteristics of high-speed railway (HSR) systems is of essential significance in theory and practice for the planning, construction, and operational management of HSR systems. In this paper, the HSR system is described as a temporal network, and the [...] Read more.

Deeply understanding the dynamic operating characteristics of high-speed railway (HSR) systems is of essential significance in theory and practice for the planning, construction, and operational management of HSR systems. In this paper, the HSR system is described as a temporal network, and the evolution of connected clusters in the system is considered as a percolation process. The critical integration time $T_c$ of the percolation process can determine the formation of a globally connected cluster and measure the transport performance of the HSR system. The appearance time of critical edges identified at $T_c$ can significantly affect the reliability of the transport performance of an HSR system. Compared to random percolation in the static HSR network, it can be found that the critical fraction $p_c$ of the percolation process in a temporal HSR network is almost always larger. This indicates that the global connectivity and the transport performance of HSR systems is overestimated by the static network abstraction. This paper provides a promising way of understanding the dynamic characteristics of HSR systems, evaluating their transport performance, and improving their reliability. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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13 pages, 3228 KiB  

Open AccessArticle

Overlapping Community Hiding Method Based on Multi-Level Neighborhood Information

by Guoliang Yang, Yanwei Wang, Zhengchao Chang and Dong Liu

Symmetry 2022, 14(11), 2328; https://doi.org/10.3390/sym14112328 - 5 Nov 2022

Cited by 4 | Viewed by 1777

Abstract

The overlapping community detection algorithm divides social networks into multiple overlapping parts, and members can belong to multiple communities at the same time. Although the overlapping community detection algorithm can help people understand network topology, it exposes personal privacy. The BIH algorithm is [...] Read more.

The overlapping community detection algorithm divides social networks into multiple overlapping parts, and members can belong to multiple communities at the same time. Although the overlapping community detection algorithm can help people understand network topology, it exposes personal privacy. The BIH algorithm is proposed to solve the problem of personal privacy leaks in overlapping areas. However, some specific members in overlapping areas do not want to be discovered to belong to some specific community. To solve this problem, an overlapping community hiding algorithm based on multi level neighborhood information (MLNI) is proposed. The MLNI algorithm defines node probability of community based on multi-layer neighborhood information. By adjusting the probability of the target node belonging to each community, the difference between the probability that the target node belongs to outside and inside the target community is maximized. This process can be regarded as an optimization problem. In addition, the MLNI algorithm uses the genetic algorithm to find the optimal solution, and finally achieves the purpose of moving the target node in the overlapping area out of a specific community. The effectiveness of the MLNI algorithm is demonstrated through extensive experiments and baseline algorithms. The MLNI algorithm effectively realizes the protection of personal privacy in social networks. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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9 pages, 327 KiB  

Open AccessArticle

Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control

by Rui Kang and Shang Gao

Mathematics 2022, 10(18), 3329; https://doi.org/10.3390/math10183329 - 14 Sep 2022

Viewed by 1476

Abstract

This paper investigates the stabilization for stochastic coupled Kuramoto oscillators (SCKOs) via nonlinear distributed feedback control. An original nonlinear distributed feedback control with the advantages of fast response, no steady-state deviation, and easy implementation is designed to stabilize SCKOs. With the help of [...] Read more.

This paper investigates the stabilization for stochastic coupled Kuramoto oscillators (SCKOs) via nonlinear distributed feedback control. An original nonlinear distributed feedback control with the advantages of fast response, no steady-state deviation, and easy implementation is designed to stabilize SCKOs. With the help of the Lyapunov method and stochastic analysis skills, some novel sufficient conditions guaranteeing the stochastic stability for SCKOs are provided by constructing a new and suitable Lyapunov function for SCKOs. Finally, a numerical example is given to illustrate the effectiveness and applicability of the theoretical result. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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26 pages, 2391 KiB  

Open AccessArticle

Studying Asymmetric Structure in Directed Networks by Overlapping and Non-Overlapping Models

by Huan Qing

Entropy 2022, 24(9), 1216; https://doi.org/10.3390/e24091216 - 30 Aug 2022

Cited by 1 | Viewed by 1670

Abstract

We consider the problem of modeling and estimating communities in directed networks. Models to this problem in the previous literature always assume that the sending clusters and the receiving clusters have non-overlapping property or overlapping property simultaneously. However, previous models cannot model the [...] Read more.

We consider the problem of modeling and estimating communities in directed networks. Models to this problem in the previous literature always assume that the sending clusters and the receiving clusters have non-overlapping property or overlapping property simultaneously. However, previous models cannot model the directed network in which nodes in sending clusters have overlapping property, while nodes in receiving clusters have non-overlapping property, especially for the case when the number of sending clusters is no larger than that of the receiving clusters. This kind of directed network exists in the real world for its randomness, and by the fact that we have little prior knowledge of the community structure for some real-world directed networks. To study the asymmetric structure for such directed networks, we propose a flexible and identifiable Overlapping and Non-overlapping model (ONM). We also provide one model as an extension of ONM to model the directed network, with a variation in node degree. Two spectral clustering algorithms are designed to fit the models. We establish a theoretical guarantee on the estimation consistency for the algorithms under the proposed models. A small scale computer-generated directed networks are designed and conducted to support our theoretical results. Four real-world directed networks are used to illustrate the algorithms, and the results reveal the existence of highly mixed nodes and the asymmetric structure for these networks. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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10 pages, 571 KiB  

Open AccessFeature PaperArticle

Tumor Biochemical Heterogeneity and Cancer Radiochemotherapy: Network Breakdown Zone-Model

by Argyris Dimou, Panos Argyrakis and Raoul Kopelman

Entropy 2022, 24(8), 1069; https://doi.org/10.3390/e24081069 - 2 Aug 2022

Viewed by 1825

Abstract

Breakdowns of two-zone random networks of the Erdős–Rényi type are investigated. They are used as mathematical models for understanding the incompleteness of the tumor network breakdown under radiochemotherapy, an incompleteness that may result from a tumor’s physical and/or chemical heterogeneity. Mathematically, having a [...] Read more.

Breakdowns of two-zone random networks of the Erdős–Rényi type are investigated. They are used as mathematical models for understanding the incompleteness of the tumor network breakdown under radiochemotherapy, an incompleteness that may result from a tumor’s physical and/or chemical heterogeneity. Mathematically, having a reduced node removal probability in the network’s inner zone hampers the network’s breakdown. The latter is described quantitatively as a function of reduction in the inner zone’s removal probability, where the network breakdown is described in terms of the largest remaining clusters and their size distributions. The effects on the efficacy of radiochemotherapy due to the tumor micro-environment (TME)’s chemical make-up, and its heterogeneity, are discussed, with the goal of using such TME chemical heterogeneity imaging to inform precision oncology. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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18 pages, 1460 KiB  

Open AccessArticle

Scalably Using Node Attributes and Graph Structure for Node Classification

by Arpit Merchant, Ananth Mahadevan and Michael Mathioudakis

Entropy 2022, 24(7), 906; https://doi.org/10.3390/e24070906 - 30 Jun 2022

Cited by 1 | Viewed by 1826

Abstract

The task of node classification concerns a network where nodes are associated with labels, but labels are known only for some of the nodes. The task consists of inferring the unknown labels given the known node labels, the structure of the network, and [...] Read more.

The task of node classification concerns a network where nodes are associated with labels, but labels are known only for some of the nodes. The task consists of inferring the unknown labels given the known node labels, the structure of the network, and other known node attributes. Common node classification approaches are based on the assumption that adjacent nodes have similar attributes and, therefore, that a node’s label can be predicted from the labels of its neighbors. While such an assumption is often valid (e.g., for political affiliation in social networks), it may not hold in some cases. In fact, nodes that share the same label may be adjacent but differ in their attributes, or may not be adjacent but have similar attributes. In this work, we present JANE (Jointly using Attributes and Node Embeddings), a novel and principled approach to node classification that flexibly adapts to a range of settings wherein unknown labels may be predicted from known labels of adjacent nodes in the network, other node attributes, or both. Our experiments on synthetic data highlight the limitations of benchmark algorithms and the versatility of JANE. Further, our experiments on seven real datasets of sizes ranging from 2.5K to 1.5M nodes and edge homophily ranging from 0.86 to 0.29 show that JANE scales well to large networks while also demonstrating an up to 20% improvement in accuracy compared to strong baseline algorithms. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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19 pages, 1504 KiB  

Open AccessArticle

Joint Detection of Community and Structural Hole Spanner of Networks in Hyperbolic Space

by Qi Nie, Hao Jiang, Si-Dong Zhong, Qiang Wang, Juan-Juan Wang, Hao Wang and Li-Hua Wu

Entropy 2022, 24(7), 894; https://doi.org/10.3390/e24070894 - 29 Jun 2022

Cited by 1 | Viewed by 2563

Abstract

Community detection and structural hole spanner (the node bridging different communities) identification, revealing the mesoscopic and microscopic structural properties of complex networks, have drawn much attention in recent years. As the determinant of mesoscopic structure, communities and structural hole spanners discover the clustering [...] Read more.

Community detection and structural hole spanner (the node bridging different communities) identification, revealing the mesoscopic and microscopic structural properties of complex networks, have drawn much attention in recent years. As the determinant of mesoscopic structure, communities and structural hole spanners discover the clustering and hierarchy of networks, which has a key impact on transmission phenomena such as epidemic transmission, information diffusion, etc. However, most existing studies address the two tasks independently, which ignores the structural correlation between mesoscale and microscale and suffers from high computational costs. In this article, we propose an algorithm for simultaneously detecting communities and structural hole spanners via hyperbolic embedding (SDHE). Specifically, we first embed networks into a hyperbolic plane, in which, the angular distribution of the nodes reveals community structures of the embedded network. Then, we analyze the critical gap to detect communities and the angular region where structural hole spanners may exist. Finally, we identify structural hole spanners via two-step connectivity. Experimental results on synthetic networks and real networks demonstrate the effectiveness of our proposed algorithm compared with several state-of-the-art methods. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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15 pages, 1012 KiB  

Open AccessArticle

Popularity of Video Games and Collective Memory

by Leonardo O. Mendes, Leonardo R. Cunha and Renio S. Mendes

Entropy 2022, 24(7), 860; https://doi.org/10.3390/e24070860 - 23 Jun 2022

Cited by 6 | Viewed by 5517

Abstract

Describing the permanence of cultural objects is an important step in understanding societal trends. A relatively novel cultural object is the video game, which is an interactive media, that is, the player is an active contributor to the overall experience. This article aims [...] Read more.

Describing the permanence of cultural objects is an important step in understanding societal trends. A relatively novel cultural object is the video game, which is an interactive media, that is, the player is an active contributor to the overall experience. This article aims to investigate video game permanence in collective memory using their popularity as a proxy, employing data based on the Steam platform from July 2012 to December 2020. The objectives include characterizing the database; studying the growth of players, games, and game categories; providing a model for the relative popularity distribution; and applying this model in three strata, global, major categories, and among categories. We detected linear growth trends in the number of players and the number of categories, and an exponential trend in the number of games released. Furthermore, we verified that lognormal distributions, emerging from multiplicative processes, provide a first approximation for the popularity in all strata. In addition, we proposed an improvement via Box–Cox transformations with similar parameters (from $-0.12$ ($95\%$ CI: $-0.18$, $-0.07$) to $-0.04$ ($95\%$ CI: $-0.08$, 0)). We were able to justify this improved model by interpreting the magnitude of each Box–Cox parameter as a measure of memory effects. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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14 pages, 5344 KiB  

Open AccessArticle

Spatial Distribution of Multi-Fractal Scaling Behaviours of Atmospheric XCO₂ Concentration Time Series during 2010–2018 over China

by Yiran Ma, Xinyi He, Rui Wu and Chenhua Shen

Entropy 2022, 24(6), 817; https://doi.org/10.3390/e24060817 - 11 Jun 2022

Cited by 2 | Viewed by 2354

Abstract

Exploring the spatial distribution of the multi-fractal scaling behaviours in atmospheric CO₂ concentration time series is useful for understanding the dynamic mechanisms of carbon emission and absorption. In this work, we utilise a well-established multi-fractal detrended fluctuation analysis to examine the multi-fractal [...] Read more.

Exploring the spatial distribution of the multi-fractal scaling behaviours in atmospheric CO₂ concentration time series is useful for understanding the dynamic mechanisms of carbon emission and absorption. In this work, we utilise a well-established multi-fractal detrended fluctuation analysis to examine the multi-fractal scaling behaviour of a column-averaged dry-air mole fraction of carbon dioxide (XCO₂) concentration time series over China, and portray the spatial distribution of the multi-fractal scaling behaviour. As XCO₂ data values from the Greenhouse Gases Observing Satellite (GOSAT) are insufficient, a spatio-temporal thin plate spline interpolation method is applied. The results show that XCO₂ concentration records over almost all of China exhibit a multi-fractal nature. Two types of multi-fractal sources are detected. One is long-range correlations, and the other is both long-range correlations and a broad probability density function; these are mainly distributed in southern and northern China, respectively. The atmospheric temperature and carbon emission/absorption are two possible external factors influencing the multi-fractality of the atmospheric XCO₂ concentration. Highlight: (1) An XCO₂ concentration interpolation is conducted using a spatio-temporal thin plate spline method. (2) The spatial distribution of the multi-fractality of XCO₂ concentration over China is shown. (3) Multi-fractal sources and two external factors affecting multi-fractality are analysed. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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22 pages, 929 KiB  

Open AccessArticle

Novel Methods for the Global Synchronization of the Complex Dynamical Networks with Fractional-Order Chaotic Nodes

by Yifan Zhang, Tianzeng Li, Zhiming Zhang and Yu Wang

Mathematics 2022, 10(11), 1928; https://doi.org/10.3390/math10111928 - 4 Jun 2022

Cited by 1 | Viewed by 1784

Abstract

The global synchronization of complex networks with fractional-order chaotic nodes is investigated via a simple Lyapunov function and the feedback controller in this paper. Firstly, the GMMP method is proposed to obtain the numerical solution of the fractional-order nonlinear equation based on the [...] Read more.

The global synchronization of complex networks with fractional-order chaotic nodes is investigated via a simple Lyapunov function and the feedback controller in this paper. Firstly, the GMMP method is proposed to obtain the numerical solution of the fractional-order nonlinear equation based on the relation of the fractional derivatives. Then, the new feedback controllers are proposed to achieve synchronization between the complex networks with the fractional-order chaotic nodes based on feedback control. We propose some new sufficient synchronous criteria based on the Lyapunov stability and a simple Lyapunov function. By the numerical simulations of the complex networks, we find that these synchronous criteria can apply to the arbitrary complex dynamical networks with arbitrary fractional-order chaotic nodes. Numerical simulations of synchronization between two complex dynamical networks with the fractional-order chaotic nodes are given by the GMMP method and the Newton method, and the results of numerical simulation demonstrate that the proposed method is universal and effective. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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13 pages, 1326 KiB  

Open AccessArticle

Time Series Prediction of Sea Surface Temperature Based on an Adaptive Graph Learning Neural Model

by Tingting Wang, Zhuolin Li, Xiulin Geng, Baogang Jin and Lingyu Xu

Future Internet 2022, 14(6), 171; https://doi.org/10.3390/fi14060171 - 31 May 2022

Cited by 15 | Viewed by 2522

Abstract

The accurate prediction of sea surface temperature (SST) is the basis for our understanding of local and global climate characteristics. At present, the existing sea temperature prediction methods fail to take full advantage of the potential spatial dependence between variables. Among them, graph [...] Read more.

The accurate prediction of sea surface temperature (SST) is the basis for our understanding of local and global climate characteristics. At present, the existing sea temperature prediction methods fail to take full advantage of the potential spatial dependence between variables. Among them, graph neural networks (GNNs) modeled on the relationships between variables can better deal with space–time dependency issues. However, most of the current graph neural networks are applied to data that already have a good graph structure, while in SST data, the dependency relationship between spatial points needs to be excavated rather than existing as prior knowledge. In order to predict SST more accurately and break through the bottleneck of existing SST prediction methods, we urgently need to develop an adaptive SST prediction method that is independent of predefined graph structures and can take full advantage of the real temporal and spatial correlations hidden indata sets. Therefore, this paper presents a graph neural network model designed specifically for space–time sequence prediction that can automatically learn the relationships between variables and model them. The model automatically extracts the dependencies between sea temperature multi-variates by embedding the nodes of the adaptive graph learning module, so that the fine-grained spatial correlations hidden in the sequence data can be accurately captured. Figure learning modules, graph convolution modules, and time convolution modules are integrated into a unified end-to-end framework for learning. Experiments were carried out on the Bohai Sea surface temperature data set and the South China Sea surface temperature data set, and the results show that the model presented in this paper is significantly better than other sea temperature model predictions in two remote-sensing sea temperature data sets and the surface temperature of the South China Sea is easier to predict than the surface temperature of the Bohai Sea. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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14 pages, 3337 KiB  

Open AccessArticle

Learning Coupled Oscillators System with Reservoir Computing

by Xijuan Zhong and Shuai Wang

Symmetry 2022, 14(6), 1084; https://doi.org/10.3390/sym14061084 - 25 May 2022

Cited by 7 | Viewed by 2497

Abstract

In this paper, we reconstruct the dynamic behavior of the ring-coupled Lorenz oscillators system by reservoir computing. Although the reconstruction of various complex chaotic attractors has been well studied by using various neural networks, little attention has been paid to whether the spatio-temporal [...] Read more.

In this paper, we reconstruct the dynamic behavior of the ring-coupled Lorenz oscillators system by reservoir computing. Although the reconstruction of various complex chaotic attractors has been well studied by using various neural networks, little attention has been paid to whether the spatio-temporal structure of some special attractors can be maintained in long-term prediction. Reservoir computing has been shown to be effective for model-free prediction, so we want to investigate whether reservoir computing can restore the rotational symmetry of the original ring-coupled Lorenz system. We find that although the state prediction of the trained reservoir computer will gradually deviate from the actual trajectory of the original system, the associated spatio-temporal structure is maintained in the process of reconstruction. Specifically, we show that the rotational symmetric structure of periodic rotating waves, quasi-periodic torus, and chaotic rotating waves is well maintained. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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14 pages, 447 KiB  

Open AccessArticle

Topology Identification of Time-Scales Complex Networks

by Yong Pei, Churong Chen and Dechang Pi

Mathematics 2022, 10(10), 1755; https://doi.org/10.3390/math10101755 - 21 May 2022

Viewed by 1757

Abstract

This paper studies a topology identification problem of complex networks with dynamics on different time scales. Using the adaptive synchronization method, some criteria for a successful estimation are obtained. In particular, by regulating the original network to synchronize with an auxiliary chaotic network, [...] Read more.

This paper studies a topology identification problem of complex networks with dynamics on different time scales. Using the adaptive synchronization method, some criteria for a successful estimation are obtained. In particular, by regulating the original network to synchronize with an auxiliary chaotic network, this work further explores a way to avoid the precondition of linear independence. When the adaptive controller fails to achieve the outer synchronization, an impulsive control method is used. In the end, we conclude with three numerical simulations. The results obtained in this paper generalize continuous, discrete with arbitrary time step size and mixed cases. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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23 pages, 3722 KiB  

Open AccessArticle

Behavior Variations and Their Implications for Popularity Promotions: From Elites to Mass on Weibo

by Bowen Shi, Ke Xu and Jichang Zhao

Entropy 2022, 24(5), 664; https://doi.org/10.3390/e24050664 - 9 May 2022

Cited by 1 | Viewed by 2257

Abstract

The boom in social media with regard to producing and consuming information simultaneously implies the crucial role of online user influence in determining content popularity. In particular, understanding behavior variations between the influential elites and the mass grassroots is an important issue in [...] Read more.

The boom in social media with regard to producing and consuming information simultaneously implies the crucial role of online user influence in determining content popularity. In particular, understanding behavior variations between the influential elites and the mass grassroots is an important issue in communication. However, how their behavior varies across user categories and content domains and how these differences influence content popularity are rarely addressed. From a novel view of seven content domains, a detailed picture of the behavior variations among five user groups, from the views of both the elites and mass, is drawn on Weibo, one of the most popular Twitter-like services in China. Interestingly, elites post more diverse content with video links, while the mass possess retweeters of higher loyalty. According to these variations, user-oriented actions for enhancing content popularity are discussed and testified. The most surprising finding is that the diverse content does not always bring more retweets, and the mass and elites should promote content popularity by increasing their retweeter counts and loyalty, respectively. For the first time, our results demonstrate the possibility of highly individualized strategies of popularity promotions in social media, instead of a universal principle. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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16 pages, 724 KiB  

Open AccessArticle

Event-Triggered Consensus Control of Nonlinear Strict Feedback Multi-Agent Systems

by Jiaojiao Zhuang, Zhenxing Li, Zongxiang Hou and Chengdong Yang

Mathematics 2022, 10(9), 1596; https://doi.org/10.3390/math10091596 - 8 May 2022

Cited by 5 | Viewed by 1928

Abstract

In this paper, we investigate the event-triggered consensus problems of nonlinear strict feedback MASs under directed graph. Based on the high-gain control technique, we firstly give a state-based event-triggered consensus algorithm and prove that Zeno behavior can be excluded. When the full state [...] Read more.

In this paper, we investigate the event-triggered consensus problems of nonlinear strict feedback MASs under directed graph. Based on the high-gain control technique, we firstly give a state-based event-triggered consensus algorithm and prove that Zeno behavior can be excluded. When the full state information is unavailable, a high-gain observer is given to estimate state information of each agent and an observer-based algorithm is developed. Finally, we give an example to verify the effectiveness of both state-based and observer-based event-triggered consensus algorithms. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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21 pages, 1900 KiB  

Open AccessFeature PaperArticle

Grand Canonical Ensembles of Sparse Networks and Bayesian Inference

by Ginestra Bianconi

Entropy 2022, 24(5), 633; https://doi.org/10.3390/e24050633 - 30 Apr 2022

Cited by 7 | Viewed by 3222

Abstract

Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical [...] Read more.

Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical models for exchangeable networks in the sparse limit, i.e., with the total number of links scaling linearly with the total number of nodes. The approach is grand canonical, i.e., the number of nodes of the network is not fixed a priori: it is finite but can be arbitrarily large. In this way the grand canonical network ensembles circumvent the difficulties in treating infinite sparse exchangeable networks which according to the Aldous-Hoover theorem must vanish. The approach can treat networks with given degree distribution or networks with given distribution of latent variables. When only a subgraph induced by a subset of nodes is known, this model allows a Bayesian estimation of the network size and the degree sequence (or the sequence of latent variables) of the entire network which can be used for network reconstruction. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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Open AccessArticle

ieHDDP: An Integrated Solution for Topology Discovery and Automatic In-Band Control Channel Establishment for Hybrid SDN Environments

by Joaquin Alvarez-Horcajo, Isaias Martinez-Yelmo, Elisa Rojas, Juan Antonio Carral and David Carrascal

Symmetry 2022, 14(4), 756; https://doi.org/10.3390/sym14040756 - 6 Apr 2022

Cited by 3 | Viewed by 2316

Abstract

In-Band enhanced Hybrid Domain Discovery Protocol (ieHDDP) is a novel integral approach for hybrid Software-Defined Networking (SDN) environments that simultaneously provides a topology discovery service and an autonomous control channel configuration in the band. This contribution is particularly relevant since, to the best [...] Read more.

In-Band enhanced Hybrid Domain Discovery Protocol (ieHDDP) is a novel integral approach for hybrid Software-Defined Networking (SDN) environments that simultaneously provides a topology discovery service and an autonomous control channel configuration in the band. This contribution is particularly relevant since, to the best of our knowledge, it is the first all-in-one proposal for SDN capable of collecting the entire topology information (type of devices, links, etc.) and establishing in-band control channels at once in hybrid SDN environments (composed by SDN/no-SDN, wired/wireless devices), even with isolated SDN devices. ieHDDP facilitates the integration of heterogeneous networks, for example, in 5G/6G scenarios, and the deployment of SDN devices by using a simple exploration mechanism to gather all the required topological information and learn the necessary routes between the control and data planes at the same time. ieHDDP has been implemented in a well-known SDN software switch and evaluated in a comprehensive set of randomized topologies, acknowledging that ieHDDP is scalable in representative scenarios. Full article

(This article belongs to the Topic Complex Systems and Network Science)

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