Virtual Capacity and Dimensioning Issues in Multilayer Networks

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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Networks

10.1093/oso/9780198821939.003.0004 ◽

2018 ◽

Author(s):

Stefan Thurner ◽

Rudolf Hanel ◽

Peter Klimekl

Keyword(s):

Complex Systems ◽

Complex Networks ◽

Phase Diagrams ◽

Community Detection ◽

Network Science ◽

Small World ◽

Small World Networks ◽

Multilayer Networks ◽

Basic Vocabulary

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.

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The structure of co-publications multilayer network

Computational Social Networks ◽

10.1186/s40649-021-00089-w ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Ghislain Romaric Meleu ◽

Paulin Yonta Melatagia

Keyword(s):

Power Law ◽

Degree Distribution ◽

Preferential Attachment ◽

Small World ◽

Generation Model ◽

Small World Network ◽

Power Law Distribution ◽

Multilayer Networks ◽

Multilayer Network ◽

Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

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