Complex Networks and Social Networks

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Algorithms algorithms	1.8	4.1	2008	15 Days	CHF 1600
Computation computation	1.9	3.5	2013	19.7 Days	CHF 1800
Information information	2.4	6.9	2010	14.9 Days	CHF 1600
Mathematics mathematics	2.3	4.0	2013	17.1 Days	CHF 2600

22 pages, 2570 KiB

Open AccessArticle

Vulnerability Analysis of a Multilayer Logistics Network against Cascading Failure

by Tongyu Wu, Minjie Li and Shuangjiao Lin

Algorithms 2024, 17(9), 414; https://doi.org/10.3390/a17090414 - 19 Sep 2024

Viewed by 704

One of the most challenging issues in contemporary complex network research is to understand the structure and vulnerability of multilayer networks, even though cascading failures in single networks have been widely studied in recent years. The goal of this work is to compare [...] Read more.

One of the most challenging issues in contemporary complex network research is to understand the structure and vulnerability of multilayer networks, even though cascading failures in single networks have been widely studied in recent years. The goal of this work is to compare the similarities and differences between four single layers and understand the implications of interdependencies among cities on the overall vulnerability of a multilayer global logistics network. In this paper, a global logistics network model set as a multilayer network considering cascading failures is proposed in different disruption scenarios. Two types of attack strategies—a highest load attack and a lowest load attack—are used to evaluate the vulnerability of the global logistics network and to further analyze the changes in the topology properties. For a multilayer network, the vulnerability of single layers is compared as well. The results suggest that compared with the results of a single global logistics network, a multilayer network has a higher vulnerability. In addition, the heterogeneity of networks plays an important role in the vulnerability of a multilayer network against targeted attacks. Protecting the most important nodes is critical to safeguard the potential “vulnerability” in the development of the global logistics network. The three-step response strategy of “Prewarning–Response–Postrepair” is the main pathway to improving the adjustment ability and adaptability of logistics hub cities in response to external shocks. These findings supplement and extend the previous attack results on nodes and can thus help us better explain the vulnerability of different networks and provide insight into more tolerant, real, complex system designs. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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14 pages, 371 KiB

Open AccessArticle

Complex Network Model of Global Financial Time Series Based on Different Distance Functions

by Zhen Wang, Jicai Ning and Meng Gao

Mathematics 2024, 12(14), 2210; https://doi.org/10.3390/math12142210 - 15 Jul 2024

Cited by 1 | Viewed by 669

Abstract

By constructing a complex network model grounded in time series analysis, this study delves into the intricate relationships between the stock markets of 18 countries worldwide. Utilizing 31 distinct time series distance functions to formulate the network, we employ Hamming distance to quantify [...] Read more.

By constructing a complex network model grounded in time series analysis, this study delves into the intricate relationships between the stock markets of 18 countries worldwide. Utilizing 31 distinct time series distance functions to formulate the network, we employ Hamming distance to quantify the resemblance between networks derived from different distance functions. By modulating the network density through distance percentiles (

p = 0.1

, 0.3, 0.5), we demonstrate the similarity of various distance functions across multiple density levels. Our findings reveal that certain distance functions exhibit high degrees of similarity across varying network densities, suggesting their potential for mutual substitution in network construction. Furthermore, the centroid network identified via hierarchical cluster analysis highlights the similarities between the stock markets of different nations, mirroring the intricate interconnections within the global financial landscape. The insights gained from this study offer crucial perspectives for comprehending the intricate network structure of global financial time series data, paving the way for further analysis and prediction of global financial market dynamics. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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13 pages, 1010 KiB

Open AccessArticle

Static Bipartite Consensus Problems of Heterogeneous Signed Networks

by Yu Ma, Yi Zhang, Jinchao Li, Mingjun Du and Peng Ji

Mathematics 2024, 12(10), 1523; https://doi.org/10.3390/math12101523 - 14 May 2024

Viewed by 740

Abstract

This paper aims to study the distributed control problems of heterogeneous signed networks whose communication topologies are undirected. A distributed control protocol is designed based on neighboring state information. With this protocol be employed, the convergence results of the heterogeneous signed network are [...] Read more.

This paper aims to study the distributed control problems of heterogeneous signed networks whose communication topologies are undirected. A distributed control protocol is designed based on neighboring state information. With this protocol be employed, the convergence results of the heterogeneous signed network are provided. It is shown that the heterogeneous signed network can achieve the static bipartite consensus (respectively, state stability) if and only if the signed graph is structurally balanced (respectively, unbalanced). The associated convergence analyses can be developed by constructing a suitable Lyapunov function. In addition, two simulation examples are presented to validate the correctness of the obtained results. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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15 pages, 499 KiB

Open AccessArticle

Revolutionary Strategy for Depicting Knowledge Graphs with Temporal Attributes

by Sihan Li and Qi Li

Mathematics 2024, 12(9), 1324; https://doi.org/10.3390/math12091324 - 26 Apr 2024

Viewed by 842

Abstract

In practical applications, the temporal completeness of knowledge graphs is of great importance. However, previous studies have mostly focused on static knowledge graphs, generally neglecting the dynamic evolutionary properties of facts. Moreover, the unpredictable and limited availability of temporal knowledge graphs, together with [...] Read more.

In practical applications, the temporal completeness of knowledge graphs is of great importance. However, previous studies have mostly focused on static knowledge graphs, generally neglecting the dynamic evolutionary properties of facts. Moreover, the unpredictable and limited availability of temporal knowledge graphs, together with the complex temporal dependency patterns, make current models inadequate for effectively describing facts that experience temporal transitions. To better represent the evolution of things over time, we provide a learning technique that uses quaternion rotation to describe temporal knowledge graphs. This technique describes the evolution of entities as a temporal rotation change in quaternion space. Compared to the Ermitian inner product in complex number space, the Hamiltonian product in quaternion space is better at showing how things might be connected. This leads to a learning process that is both more effective and more articulate. Experimental results demonstrate that our learning method significantly outperforms existing methods in capturing the dynamic evolution of temporal knowledge graphs, with improved accuracy and robustness across a range of benchmark datasets. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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16 pages, 460 KiB

Open AccessArticle

Bipartite Consensus Problems for Directed Signed Networks with External Disturbances

by Baoyu Huo, Jian Ma and Mingjun Du

Mathematics 2023, 11(23), 4828; https://doi.org/10.3390/math11234828 - 30 Nov 2023

Viewed by 1082

Abstract

The intention of this paper is to explore the distributed control issues for directed signed networks in the face of external disturbances under strongly connected topologies. A new class of nonsingular transformations is provided by introducing an output variable, with which the consensus [...] Read more.

The intention of this paper is to explore the distributed control issues for directed signed networks in the face of external disturbances under strongly connected topologies. A new class of nonsingular transformations is provided by introducing an output variable, with which the consensus can be equivalently transformed into the output stability regardless of whether the associated signed digraphs are structurally balanced or not. By taking advantage of the standard robust

H_{\infty}

control theory, the bipartite consensus and state stability results can be built for signed networks under structurally balanced and unbalanced conditions, respectively, in which the desired disturbance rejection performances can also be satisfied. Furthermore, the mathematical expression can be given for the terminal states of signed networks under the influence of external disturbances. In addition, two simulations are presented to verify the correctness of our developed results. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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22 pages, 1036 KiB

Open AccessArticle

Logical–Mathematical Foundations of a Graph Query Framework for Relational Learning

by Pedro Almagro-Blanco, Fernando Sancho-Caparrini and Joaquín Borrego-Díaz

Mathematics 2023, 11(22), 4672; https://doi.org/10.3390/math11224672 - 16 Nov 2023

Viewed by 1063

Abstract

Relational learning has attracted much attention from the machine learning community in recent years, and many real-world applications have been successfully formulated as relational learning problems. In recent years, several relational learning algorithms have been introduced that follow a pattern-based approach. However, this [...] Read more.

Relational learning has attracted much attention from the machine learning community in recent years, and many real-world applications have been successfully formulated as relational learning problems. In recent years, several relational learning algorithms have been introduced that follow a pattern-based approach. However, this type of learning model suffers from two fundamental problems: the computational complexity arising from relational queries and the lack of a robust and general framework to serve as the basis for relational learning methods. In this paper, we propose an efficient graph query framework that allows for cyclic queries in polynomial time and is ready to be used in pattern-based learning methods. This solution uses logical predicates instead of graph isomorphisms for query evaluation, reducing complexity and allowing for query refinement through atomic operations. The main differences between our method and other previous pattern-based graph query approaches are the ability to evaluate arbitrary subgraphs instead of nodes or complete graphs, the fact that it is based on mathematical formalization that allows the study of refinements and their complementarity, and the ability to detect cyclic patterns in polynomial time. Application examples show that the proposed framework allows learning relational classifiers to be efficient in generating data with high expressiveness capacities. Specifically, relational decision trees are learned from sets of tagged subnetworks that provide both classifiers and characteristic patterns for the identified classes. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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19 pages, 1222 KiB

Open AccessArticle

Discrete versus Continuous Algorithms in Dynamics of Affective Decision Making

by Vyacheslav I. Yukalov and Elizaveta P. Yukalova

Algorithms 2023, 16(9), 416; https://doi.org/10.3390/a16090416 - 29 Aug 2023

Viewed by 1609

Abstract

The dynamics of affective decision making is considered for an intelligent network composed of agents with different types of memory: long-term and short-term memory. The consideration is based on probabilistic affective decision theory, which takes into account the rational utility of alternatives as [...] Read more.

The dynamics of affective decision making is considered for an intelligent network composed of agents with different types of memory: long-term and short-term memory. The consideration is based on probabilistic affective decision theory, which takes into account the rational utility of alternatives as well as the emotional alternative attractiveness. The objective of this paper is the comparison of two multistep operational algorithms of the intelligent network: one based on discrete dynamics and the other on continuous dynamics. By means of numerical analysis, it is shown that, depending on the network parameters, the characteristic probabilities for continuous and discrete operations can exhibit either close or drastically different behavior. Thus, depending on which algorithm is employed, either discrete or continuous, theoretical predictions can be rather different, which does not allow for a uniquely defined description of practical problems. This finding is important for understanding which of the algorithms is more appropriate for the correct analysis of decision-making tasks. A discussion is given, revealing that the discrete operation seems to be more realistic for describing intelligent networks as well as affective artificial intelligence. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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12 pages, 410 KiB

Open AccessArticle

Subdomination in Graphs with Upper-Bounded Vertex Degree

by Darya Lemtyuzhnikova, Pavel Chebotarev, Mikhail Goubko, Ilja Kudinov and Nikita Shushko

Mathematics 2023, 11(12), 2722; https://doi.org/10.3390/math11122722 - 15 Jun 2023

Cited by 1 | Viewed by 1063

Abstract

We find a lower bound for the k-subdomination number on the set of graphs with a given upper bound for vertex degrees. We study the cases where the proposed lower bound is sharp, construct the optimal graphs and indicate the corresponding k [...] Read more.

We find a lower bound for the k-subdomination number on the set of graphs with a given upper bound for vertex degrees. We study the cases where the proposed lower bound is sharp, construct the optimal graphs and indicate the corresponding k-subdominating functions. The results are interpreted in terms of social structures. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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16 pages, 725 KiB

Open AccessArticle

Deep Cross-Network Alignment with Anchor Node Pair Diverse Local Structure

by Yinghui Wang, Wenjun Wang, Minglai Shao and Yueheng Sun

Algorithms 2023, 16(5), 234; https://doi.org/10.3390/a16050234 - 28 Apr 2023

Viewed by 1710

Abstract

Network alignment (NA) offers a comprehensive way to build associations between different networks by identifying shared nodes. While the majority of current NA methods rely on the topological consistency assumption, which posits that shared nodes across different networks typically have similar local structures [...] Read more.

Network alignment (NA) offers a comprehensive way to build associations between different networks by identifying shared nodes. While the majority of current NA methods rely on the topological consistency assumption, which posits that shared nodes across different networks typically have similar local structures or neighbors, we argue that anchor nodes, which play a pivotal role in NA, face a more challenging scenario that is often overlooked. In this paper, we conduct extensive statistical analysis across networks to investigate the connection status of labeled anchor node pairs and categorize them into four situations. Based on our analysis, we propose an end-to-end network alignment framework that uses node representations as a distribution rather than a point vector to better handle the structural diversity of networks. To mitigate the influence of specific nodes, we introduce a mask mechanism during the representation learning process. In addition, we utilize meta-learning to generalize the learned information on labeled anchor node pairs to other node pairs. Finally, we perform comprehensive experiments on both real-world and synthetic datasets to confirm the efficacy of our proposed method. The experimental results demonstrate that the proposed model outperforms the state-of-the-art methods significantly. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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29 pages, 2155 KiB

Open AccessArticle

Stability, Hopf Bifurcation and Optimal Control of Multilingual Rumor-Spreading Model with Isolation Mechanism

by Shuzhen Yu, Zhiyong Yu and Haijun Jiang

Mathematics 2022, 10(23), 4556; https://doi.org/10.3390/math10234556 - 1 Dec 2022

Cited by 2 | Viewed by 1534

Abstract

The propagation of rumors on online social networks (OSNs) brings an awful lot of trouble to people’s life and society. Aiming at combating rumors spreading on OSNs, two novel rumor-propagation models without and with time delays are proposed, which combine with the influence [...] Read more.

The propagation of rumors on online social networks (OSNs) brings an awful lot of trouble to people’s life and society. Aiming at combating rumors spreading on OSNs, two novel rumor-propagation models without and with time delays are proposed, which combine with the influence of the immune mechanism, isolation mechanism and network structure. Firstly, we analyze the existence of rumor equilibria and obtain some existence conditions of backward bifurcation. Secondly, the local stabilities of rumor-free and rumor equilibria are proved by using the Jacobian matrix method, and some critical conditions for the existence of Hopf bifurcation are acquired by selecting critical parameters and delays as bifurcation parameters. Furthermore, an optimal control method is proposed, which can prevent the spread of rumors within an expected time period and minimize the cost of control. Finally, some numerical simulations are provided to verify the effectiveness of the proposed theoretical results. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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14 pages, 412 KiB

Open AccessArticle

Monitoring Sparse and Attributed Network Streams with MultiLevel and Dynamic Structures

by Mostafa Mostafapour, Farzad Movahedi Sobhani and Abbas Saghaei

Mathematics 2022, 10(23), 4483; https://doi.org/10.3390/math10234483 - 28 Nov 2022

Cited by 1 | Viewed by 1416

Abstract

In this study, we create a new monitoring system for change detection in sparse attributed network streams with multilevel or nested dynamic structures. To achieve this, we hypothesize that the contingency of establishing an edge between two network nodes at time t depends [...] Read more.

In this study, we create a new monitoring system for change detection in sparse attributed network streams with multilevel or nested dynamic structures. To achieve this, we hypothesize that the contingency of establishing an edge between two network nodes at time t depends on the properties of the network edges, network nodes, groups, or categories. Then, we estimate the model parameters using the expressed logit model. The model parameters are developed using the state-space model to achieve a dynamic state in the system. The extended Kalman filter (EKF) updates state-space parameters and predicts upcoming networks. Predicted residuals are tracked using statistical process control charts to identify changes in the underlying mechanism of edge generation. This research makes a methodological contribution by combining zero-inflated generalized linear mixed models (ZI-GLMMs) with the state-space model to monitor changes in the sequences of sparse, attributed, and weighted multilevel networks by applying control charts. The proposed model is compared to previous models to evaluate performance by implementing three scenarios. The results show that the model is faster at detecting the first change. Finally, using real e-MID data, we measured the model’s performance in detecting real data changes. The findings suggest that the proposed model could predict a crisis in advance of significant European Central Bank statements and events. Full article

(This article belongs to the Topic Complex Networks and Social Networks)

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