A survey of community detection methods in multilayer networks

Abstract Community detection is one of the most popular researches in a variety of complex systems, ranging from biology to sociology. In recent years, there’s an increasing focus on the rapid development of more complicated networks, namely multilayer networks. Communities in a single-layer network are groups of nodes that are more strongly connected among themselves than the others, while in multilayer networks, a group of well-connected nodes are shared in multiple layers. Most traditional algorithms can rarely perform well on a multilayer network without modifications. Thus, in this paper, we offer overall comparisons of existing works and analyze several representative algorithms, providing a comprehensive understanding of community detection methods in multilayer networks. The comparison results indicate that the promoting of algorithm efficiency and the extending for general multilayer networks are also expected in the forthcoming studies.

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OPINION DIFFUSION ON MULTILAYER SOCIAL NETWORKS

Advances in Complex Systems ◽

10.1142/s0219525917500151 ◽

2017 ◽

Vol 20 (06n07) ◽

pp. 1750015 ◽

Cited By ~ 3

Author(s):

HAI-BO HU ◽

CANG-HAI LI ◽

QING-YING MIAO

Keyword(s):

Social Networks ◽

Opinion Dynamics ◽

Coupling Agents ◽

Dynamics Model ◽

Multilayer Networks ◽

Multilayer Network ◽

Influence Matrix ◽

Strongly Connected ◽

Degroot Model ◽

Multilayer Social Networks

In this paper, to reveal the influence of multilayer network structure on opinion diffusion in social networks, we study an opinion dynamics model based on DeGroot model on multilayer networks. We find that if the influence matrix integrating the information of connectedness for each layer and correlation between layers is strongly connected and aperiodic, all agents’ opinions will reach a consensus. However, if there are stubborn agents in the networks, regular agents’ opinions will finally be confined to the convex combinations of the stubborn agents’. Specifically, if all stubborn agents hold the same opinion, even if the agents only exist on a certain layer, their opinions will diffuse to the entire multilayer networks. This paper not only characterizes the influence of multilayer network topology and agent attribute on opinion diffusion in a holistic way, but also demonstrates the importance of coupling agents which play an indispensable role in some social and economic situations.

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Complex Systems as Multilayer Networks

10.1093/oso/9780198753919.003.0001 ◽

2018 ◽

Author(s):

Ginestra Bianconi

Keyword(s):

Complex Systems ◽

Information Gain ◽

Single Layer ◽

Multilayer Networks ◽

Research Activity ◽

Multilayer Network ◽

New Development ◽

The Rich ◽

And Function

Chapter 1 constitutes Part I of the book: ‘Single and Multilayer Networks’. This chapter introduces multilayer networks as an important new development of Network Science that allows a more comprehensive understanding of Complex Systems. It identifies the main motivations driving the research activity in this field of multilayer networks and emphasizes the benefits of taking a multilayer network perpective to characterize network data. The main advantages of a multilayer network approach with respect to the more traditional single layer characterization of complex networks are broadly discussed, focusing on the information gain resulting from the analysis of multilayer networks, the non-reducibility of a multilayer network to a large single network and the rich interplay between structure and function in multilayer networks.

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Multilayer Networks

10.1093/oso/9780198753919.001.0001 ◽

2018 ◽

Cited By ~ 59

Author(s):

Ginestra Bianconi

Keyword(s):

Network Topology ◽

Multilayer Structure ◽

Data Science ◽

Transportation Systems ◽

Molecular Networks ◽

Detection Methods ◽

Multilayer Networks ◽

Multilayer Network ◽

Recent Developments ◽

Highly Correlated

Multilayer networks are formed by several networks that interact with each other and co-evolve. Multilayer networks include social networks, financial markets, transportation systems, infrastructures and molecular networks and the brain. The multilayer structure of these networks strongly affects the properties of dynamical and stochastic processes defined on them, which can display unexpected characteristics. For example, interdependencies between different networks of a multilayer structure can cause cascades of failure events that can dramatically increase the fragility of these systems; spreading of diseases, opinions and ideas might take advantage of multilayer network topology and spread even when its single layers cannot sustain an epidemic when taken in isolation; diffusion on multilayer transportation networks can significantly speed up with respect to diffusion on single layers; finally, the interplay between multiplexity and controllability of multilayer networks is a problem with major consequences in financial, transportation, molecular biology and brain networks. This field is one of the most prosperous recent developments of Network Science and Data Science. Multilayer networks include multiplex networks, multi-slice temporal networks, networks of networks, interdependent networks. Multilayer networks are characterized by having a highly correlated multilayer network structure, providing a significant advantage for extracting information from them using multilayer network measures and centralities and community detection methods. The multilayer network dynamics (including percolation, epidemic spreading, diffusion, synchronization, game theory and control) is strongly affected by the multilayer network topology. This book will present a comprehensive account of this emerging field.

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Application of Multilayer Network Models in Bioinformatics

Frontiers in Genetics ◽

10.3389/fgene.2021.664860 ◽

2021 ◽

Vol 12 ◽

Author(s):

Yuanyuan Lv ◽

Shan Huang ◽

Tianjiao Zhang ◽

Bo Gao

Keyword(s):

Evaluation Method ◽

Brain Research ◽

Single Layer ◽

Network Models ◽

Assessment Method ◽

Multilayer Networks ◽

Multilayer Network ◽

Biological Studies ◽

Quality Assessment Method ◽

Object Of Study

Multilayer networks provide an efficient tool for studying complex systems, and with current, dramatic development of bioinformatics tools and accumulation of data, researchers have applied network concepts to all aspects of research problems in the field of biology. Addressing the combination of multilayer networks and bioinformatics, through summarizing the applications of multilayer network models in bioinformatics, this review classifies applications and presents a summary of the latest results. Among them, we classify the applications of multilayer networks according to the object of study. Furthermore, because of the systemic nature of biology, we classify the subjects into several hierarchical categories, such as cells, tissues, organs, and groups, according to the hierarchical nature of biological composition. On the basis of the complexity of biological systems, we selected brain research for a detailed explanation. We describe the application of multilayer networks and chronological networks in brain research to demonstrate the primary ideas associated with the application of multilayer networks in biological studies. Finally, we mention a quality assessment method focusing on multilayer and single-layer networks as an evaluation method emphasizing network studies.

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Opinion Dynamics and Game Theory

10.1093/oso/9780198753919.003.0016 ◽

2018 ◽

Author(s):

Ginestra Bianconi

Keyword(s):

Game Theory ◽

Social Systems ◽

Single Layer ◽

Opinion Dynamics ◽

Structure And Function ◽

Voter Model ◽

Multilayer Networks ◽

Multilayer Network ◽

The Rich ◽

And Function

This chapter is devoted to opinion dynamics and game theory on multilayer networks. Since in social systems multilayer networks are the rule, it is particularly relevant to extend the modelling opinion dynamics to the multilayer network scenario. This chapter focuses in particular on the Voter Model, its variants, the Co-evolving Voter Model and models of competing networks, including election models showing that multiplexity has a major role in determining opinion dynamics. In particular, opinion dynamics on multilayer networks is not reducible to opinion dynamics on single layer networks. Finally, the rich interplay between structure and function in multilayer networks is discussed in the framework of game theory.

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A Feasible Community Detection Algorithm for Multilayer Networks

Symmetry ◽

10.3390/sym12020223 ◽

2020 ◽

Vol 12 (2) ◽

pp. 223

Author(s):

Dongming Chen ◽

Panpan Du ◽

Qianrong Jiang ◽

Xinyu Huang ◽

Dongqi Wang

Keyword(s):

Community Detection ◽

Real Life ◽

Detection Algorithm ◽

Label Propagation ◽

Multilayer Networks ◽

Multilayer Network ◽

Aggregation Model ◽

Propagation Algorithm ◽

Network Aggregation ◽

Community Detection Algorithm

As a more complicated network model, multilayer networks provide a better perspective for describing the multiple interactions among social networks in real life. Different from conventional community detection algorithms, the algorithms for multilayer networks can identify the underlying structures that contain various intralayer and interlayer relationships, which is of significance and remains a challenge. In this paper, aiming at the instability of the label propagation algorithm (LPA), an improved label propagation algorithm based on the SH-index (SH-LPA) is proposed. By analyzing the characteristics and deficiencies of the H-index, the SH-index is presented as an index to evaluate the importance of nodes, and the stability of the SH-LPA algorithm is verified by a series of experiments. Afterward, considering the deficiency of the existing multilayer network aggregation model, we propose an improved multilayer network aggregation model that merges two networks into a weighted single-layer network. Finally, considering the influence of the SH-index and the weight of the edge of the weighted network, a community detection algorithm (MSH-LPA) suitable for multilayer networks is exhibited in terms of the SH-LPA algorithm, and the superiority of the mentioned algorithm is verified by experimental analysis.

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Mapping flows on hypergraphs

10.21203/rs.3.rs-134751/v1 ◽

2021 ◽

Author(s):

Anton Eriksson ◽

Daniel Edler ◽

Alexis Rojas ◽

Martin Rosvall

Keyword(s):

Random Walk ◽

Community Detection ◽

Large Scale ◽

Detection Methods ◽

Centrality Measures ◽

Multilayer Network ◽

Effective Community ◽

Dynamics And Function ◽

And Function ◽

Modelling Approach

Abstract Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random walk models to hypergraphs and studied the multibody effects on flow-based centrality measures. But mapping the large-scale structure of those flows requires effective community detection methods. We derive unipartite, bipartite, and multilayer network representations of hypergraph flows and explore how they and the underlying random walk model change the number, size, depth, and overlap of identified multilevel communities. These results help researchers choose the appropriate modelling approach when mapping flows on hypergraphs.

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Multilayer network analyses as a toolkit for measuring social structure

Current Zoology ◽

10.1093/cz/zoaa079 ◽

2021 ◽

Vol 67 (1) ◽

pp. 81-99

Author(s):

Kelly R Finn

Keyword(s):

Social Structure ◽

Social Systems ◽

Deep Understanding ◽

Single Layer ◽

Mathematical Representation ◽

Multilayer Networks ◽

Multilayer Network ◽

Network Analyses ◽

Different Types ◽

Multilayer Social Networks

Abstract The formalization of multilayer networks allows for new ways to measure sociality in complex social systems, including groups of animals. The same mathematical representation and methods are widely applicable across fields and study systems, and a network can represent drastically different types of data. As such, in order to apply analyses and interpret the results in a meaningful way the researcher must have a deep understanding of what their network is representing and what parts of it are being measured by a given analysis. Multilayer social networks can represent social structure with more detail than is often present in single layer networks, including multiple “types” of individuals, interactions, or relationships, and the extent to which these types are interdependent. Multilayer networks can also encompass a wider range of social scales, which can help overcome complications that are inherent to measuring sociality. In this paper, I dissect multilayer networks into the parts that correspond to different components of social structures. I then discuss common pitfalls to avoid across different stages of multilayer network analyses—some novel and some that always exist in social network analysis but are magnified in multi-layer representations. This paper serves as a primer for building a customized toolkit of multilayer network analyses, to probe components of social structure in animal social systems.

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Diffusion

10.1093/oso/9780198753919.003.0014 ◽

2018 ◽

Author(s):

Ginestra Bianconi

Keyword(s):

Random Walks ◽

Spectral Properties ◽

Diffusion Constant ◽

Network Structures ◽

Multilayer Networks ◽

Multilayer Network ◽

Lévy Walk ◽

Number Of Layers ◽

Levy Walk ◽

Speed Up

This chapter addresses diffusion, random walks and congestion in multilayer networks. Here it is revealed that diffusion on a multilayer network can be significantly speed up with respect to diffusion taking place on its single layers taken in isolation, and that sometimes it is possible also to observe super-diffusion. Diffusion is here characterized on multilayer network structures by studying the spectral properties of the supra-Laplacian and the dependence on the diffusion constant among different layers. Random walks and its variations including the Lévy Walk are shown to reflect the improved navigability of multilayer networks with more layers. These results are here compared with the results of traffic on multilayer networks that, on the contrary, point out that increasing the number of layers could be detrimental and could lead to congestion.

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Centrality Measures

10.1093/oso/9780198753919.003.0009 ◽

2018 ◽

Author(s):

Ginestra Bianconi

Keyword(s):

State Of The Art ◽

Centrality Measures ◽

Eigenvector Centrality ◽

Multilayer Networks ◽

Comprehensive Description ◽

Multilayer Network ◽

Suitable Definition ◽

Katz Centrality ◽

Pagerank Centrality

Defining the centrality of nodes and layers in multilayer networks is of fundamental importance for a variety of applications from sociology to biology and finance. This chapter presents the state-of-the-art centrality measures able to characterize the centrality of nodes, the influences of layers or the centrality of replica nodes in multilayer and multiplex networks. These centrality measures include modifications of the eigenvector centrality, Katz centrality, PageRank centrality and Communicability to the multilayer network scenario. The chapter provides a comprehensive description of the research of the field and discusses the main advantages and limitations of the different definitions, allowing the readers that wish to apply these techniques to choose the most suitable definition for his or her case study.

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