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Complex Networks from Information Measures

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (31 July 2019) | Viewed by 23229

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Prof. Dr. Dimitris Kugiumtzis

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Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Interests: time series analysis; information measures; complex networks; complex systems; machine learning; stochastic simulation
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Special Issue Information

Dear Colleagues,

In the study of complex systems, such as brain dynamics and financial market dynamics, a main objective is the estimation of the connectivity structure of the observed variables (or subsystems). Having selected a connectivity measure to estimate the inter-dependence among the observed variables, the complex network is then formed, where the nodes are the observed variables and the connections are the estimated inter-dependences. A main stream of methods for connectivity estimation are based on information theory, focusing on the primary property of connectivity, the information processing and transfer. Information measures have been used to estimate both symmetrical (correlation) and directed (causality) inter-dependences in the observed variables. For independent observations, information measures are attractive alternatives to classical correlation measures, whereas in time series, information measures are found to generalize the Granger causality beyond linear models.

The aim of this Special Issue is to highlight the research topic of complex networks from information measures and collect original contributions on this topic. Researchers are encouraged to present recent developments on the methodology and applications of information-based complex networks, as well as comparative studies of information and other connectivity measures.

Prof. Dr. Dimitris Kugiumtzis
Guest Editor

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Keywords

information theory
complex systems
complex networks
time series
connectivity
correlation networks
information transfer
nonlinear dynamics.

Published Papers (6 papers)

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Research

24 pages, 1807 KiB

Open AccessArticle

Evaluation of Granger Causality Measures for Constructing Networks from Multivariate Time Series

by Elsa Siggiridou, Christos Koutlis, Alkiviadis Tsimpiris and Dimitris Kugiumtzis

Entropy 2019, 21(11), 1080; https://doi.org/10.3390/e21111080 - 04 Nov 2019

Cited by 33 | Viewed by 4216

Abstract

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. These measures are in the time domain, such as model-based and information measures, the frequency domain, and the phase domain. The study aims also to compare bivariate and multivariate measures, linear and nonlinear measures, as well as the use of dimension reduction in linear model-based measures and information measures. The latter is particular relevant in the study of high-dimensional time series. For the performance of the multivariate causality measures, low and high dimensional coupled dynamical systems are considered in discrete and continuous time, as well as deterministic and stochastic. The measures are evaluated and ranked according to their ability to provide causality networks that match the original coupling structure. The simulation study concludes that the Granger causality measures using dimension reduction are superior and should be preferred particularly in studies involving many observed variables, such as multi-channel electroencephalograms and financial markets. Full article

(This article belongs to the Special Issue Complex Networks from Information Measures)

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21 pages, 2964 KiB

Open AccessArticle

Quantifying the Variability in Resting-State Networks

by Isaura Oliver, Jaroslav Hlinka, Jakub Kopal and Jörn Davidsen

Entropy 2019, 21(9), 882; https://doi.org/10.3390/e21090882 - 11 Sep 2019

Cited by 13 | Viewed by 3717

Abstract

Recent precision functional mapping of individual human brains has shown that individual brain organization is qualitatively different from group average estimates and that individuals exhibit distinct brain network topologies. How this variability affects the connectivity within individual resting-state networks remains an open question. This is particularly important since certain resting-state networks such as the default mode network (DMN) and the fronto-parietal network (FPN) play an important role in the early detection of neurophysiological diseases like Alzheimer’s, Parkinson’s, and attention deficit hyperactivity disorder. Using different types of similarity measures including conditional mutual information, we show here that the backbone of the functional connectivity and the direct connectivity within both the DMN and the FPN does not vary significantly between healthy individuals for the AAL brain atlas. Weaker connections do vary however, having a particularly pronounced effect on the cross-connections between DMN and FPN. Our findings suggest that the link topology of single resting-state networks is quite robust if a fixed brain atlas is used and the recordings are sufficiently long—even if the whole brain network topology between different individuals is variable. Full article

(This article belongs to the Special Issue Complex Networks from Information Measures)

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15 pages, 2035 KiB

Open AccessArticle

A Potential Information Capacity Index for Link Prediction of Complex Networks Based on the Cannikin Law

by Xing Li, Shuxin Liu, Hongchang Chen and Kai Wang

Entropy 2019, 21(9), 863; https://doi.org/10.3390/e21090863 - 04 Sep 2019

Cited by 22 | Viewed by 4570

Abstract

Recently, a number of similarity-based methods have been proposed for link prediction of complex networks. Among these indices, the resource-allocation-based prediction methods perform very well considering the amount of resources in the information transmission process between nodes. However, they ignore the information channels and their information capacity in information transmission process between two endpoints. Motivated by the Cannikin Law, the definition of information capacity is proposed to quantify the information transmission capability between any two nodes. Then, based on the information capacity, a potential information capacity (PIC) index is proposed for link prediction. Empirical study on 15 datasets has shown that the PIC index we proposed can achieve a good performance, compared with eight mainstream baselines. Full article

(This article belongs to the Special Issue Complex Networks from Information Measures)

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13 pages, 435 KiB

Open AccessArticle

Anchor Link Prediction across Attributed Networks via Network Embedding

by Shaokai Wang, Xutao Li, Yunming Ye, Shanshan Feng, Raymond Y. K. Lau, Xiaohui Huang and Xiaolin Du

Entropy 2019, 21(3), 254; https://doi.org/10.3390/e21030254 - 06 Mar 2019

Cited by 17 | Viewed by 3890

Abstract

Presently, many users are involved in multiple social networks. Identifying the same user in different networks, also known as anchor link prediction, becomes an important problem, which can serve numerous applications, e.g., cross-network recommendation, user profiling, etc. Previous studies mainly use hand-crafted structure features, which, if not carefully designed, may fail to reflect the intrinsic structure regularities. Moreover, most of the methods neglect the attribute information of social networks. In this paper, we propose a novel semi-supervised network-embedding model to address the problem. In the model, each node of the multiple networks is represented by a vector for anchor link prediction, which is learnt with awareness of observed anchor links as semi-supervised information, and topology structure and attributes as input. Experimental results on the real-world data sets demonstrate the superiority of the proposed model compared to state-of-the-art techniques. Full article

(This article belongs to the Special Issue Complex Networks from Information Measures)

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11 pages, 584 KiB

Open AccessArticle

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

by C. T. Martínez-Martínez and J. A. Méndez-Bermúdez

Entropy 2019, 21(1), 86; https://doi.org/10.3390/e21010086 - 18 Jan 2019

Cited by 8 | Viewed by 3217

Abstract

We study the localization properties of the eigenvectors, characterized by their information entropy, of tight-binding random networks with balanced losses and gain. The random network model, which is based on Erdős–Rényi (ER) graphs, is defined by three parameters: the network size N, [...] Read more.

α

, and the losses-and-gain strength

γ

. Here, N and

α

are the standard parameters of ER graphs, while we introduce losses and gain by including complex self-loops on all vertices with the imaginary amplitude i

γ

with random balanced signs, thus breaking the Hermiticity of the corresponding adjacency matrices and inducing complex spectra. By the use of extensive numerical simulations, we define a scaling parameter

ξ \equiv ξ (N, α, γ)

that fixes the localization properties of the eigenvectors of our random network model; such that, when

ξ < 0.1

(

10 < ξ

), the eigenvectors are localized (extended), while the localization-to-delocalization transition occurs for

0.1 < ξ < 10

. Moreover, to extend the applicability of our findings, we demonstrate that for fixed

ξ

, the spectral properties (characterized by the position of the eigenvalues on the complex plane) of our network model are also universal; i.e., they do not depend on the specific values of the network parameters. Full article

(This article belongs to the Special Issue Complex Networks from Information Measures)

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14 pages, 6503 KiB

Open AccessArticle

A New Recurrence-Network-Based Time Series Analysis Approach for Characterizing System Dynamics

by Guangyu Yang, Daolin Xu and Haicheng Zhang

Entropy 2019, 21(1), 45; https://doi.org/10.3390/e21010045 - 09 Jan 2019

Cited by 7 | Viewed by 3090

Abstract

In this paper, a novel analysis method based on recurrence networks is proposed to characterize the evolution of dynamical systems. Through phase space reconstruction, a time series was transformed into a high-dimensional recurrence network and a corresponding low-dimensional recurrence network, respectively. Then, two appropriate statistics, the correlation coefficient of node degrees (CCND) and the edge similarity, were proposed to unravel the evolution properties of the considered signal. Through the investigation of the time series with distinct dynamics, different patterns in the decline rate of the CCND at different network dimensions were observed. Interestingly, an exponential scaling emerged in the CCND analysis for the chaotic time series. Moreover, it was demonstrated that the edge similarity can further characterize dynamical systems and provide detailed information on the studied time series. A method based on the fluctuation of edge similarities for neighboring edge groups was proposed to determine the number of groups that the edges should be partitioned into. Through the analysis of chaotic series corrupted by noise, it was demonstrated that both the CCND and edge similarity derived from different time series are robust under additive noise. Finally, the application of the proposed method to ventricular time series showed its effectiveness in differentiating healthy subjects from ventricular tachycardia (VT) patients. Full article

(This article belongs to the Special Issue Complex Networks from Information Measures)

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