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Book Cover
Author Cozzo, Emanuele, author.

Title Multiplex networks : basic formalism and structural properties / Emanuele Cozzo, Guilherme Ferraz de Arruda, Francisco Aparecido Rodrigues, Yamir Moreno.

Published Cham, Switzerland : Springer, [2018]


Location Call No. Status
Physical description 1 online resource : illustrations.
Series SpringerBriefs in complexity
SpringerBriefs in complexity.
Springer Physics and Astronomy eBooks 2018 English+International
Bibliography Includes bibliographical references and index.
Contents Intro; Contents; 1 Introduction; 1.1 From Simple Networks to Multiplex Networks; 2 Multiplex Networks: Basic Definition and Formalism; 2.1 Graph Representation; 2.2 Matrix Representation; 2.2.1 The Supra-Adjacency Matrix; 2.2.2 The Supra-Laplacian Matrix; 2.2.3 Multiplex Walk Matrices; 2.3 Coarse-Graining Representation of a Multiplex Network; 2.3.1 Mathematical Background; Adjacency and Laplacian Matrices; Regular Quotients; 2.3.2 The Aggregate Network; 2.3.3 The Network of Layers; 2.4 Supra-Walk Matrices and Loopless Aggregate Network; 3 Structural Metrics.
6.3.1 Supra-Laplacian Matrix6.3.1.1 Structural Transition; Bounds; Spectral Properties as a Function of the Coupling p; 6.3.2 Supra-Adjacency Matrix; Bounds; Spectral Properties as a Function of the Coupling p; 7 Tensorial Representation; 7.1 Tensorial Representation; 7.2 Tensorial Projections; 7.3 Spectral Analysis of R(λ, η); 7.3.1 Eigenvalue Problem; 7.3.2 Inverse Participation Ratio; 7.3.3 Interlacing Properties; 7.3.4 Proof of Eq.(7.9); 7.3.5 2-Layer Multiplex Case; Eigenvalue Crossing; Identical Layers; Similar Layers.
3.1 Structure of Triadic Relations in Multiplex Networks3.1.1 Triads on Multiplex Networks; 3.1.2 Expressing Clustering Coefficients Using Elementary 3-Cycles; 3.1.3 Clustering Coefficients for Aggregated Networks; 3.1.4 Clustering Coefficients in Erdős-Rényi (ER) Networks; 3.2 Transitivity in Empirical Multiplex Networks; 3.3 Subgraph Centrality; 3.3.1 Subgraph Centrality, Communicability, and Estrada Index in Single-Layer Networks; 3.3.2 Supra-Walks and Subgraph Centrality for Multiplex Networks; 4 Spectra; 4.1 The Largest Eigenvalue of the Supra-Adjacency Matrix; 4.1.1 Statistics of Walks.
4.2 Dimensionality Reduction and Spectral Properties4.2.1 Interlacing Eigenvalues; 4.2.2 Equitable Partitions; 4.2.3 Laplacian Eigenvalues; 4.3 Network of Layers and Aggregate Network; 4.4 Layer Subnetworks; 4.5 Discussion and Some Applications; 4.5.1 Adjacency Spectrum; 4.5.2 Laplacian Spectrum; 4.6 The Algebraic Connectivity; 5 Structural Organization and Transitions; 5.1 Eigengap and Structural Transitions; 5.2 The Aggregate-Equivalent Multiplex and the Structural Organization of a Multiplex Network; 5.3 Dynamical Consequences and Discussions.
5.4 Structural Transition Triggered by Layer Degradation5.5 Continuous Layers Degradation; 5.5.1 Exact Value of t* for Identical Weights; 5.5.2 General Mechanism; 5.6 Links Failure and Attacks; 5.7 The Shannon Entropy of the Fiedler Vector; 5.7.1 Transition-Like Behavior for No Node-Aligned Multiplex Networks; 6 Polynomial Eigenvalue Formulation; 6.1 Definition of the Problem; 6.1.1 Quadratic Eigenvalue Problem; 6.1.2 2-Layer Multiplex Networks; 6.2 Spectral Analysis; 6.2.1 Bounds; 6.2.2 Comments on Symmetric Problems: HQEP; 6.2.3 Limits for Sparse Inter-Layer Coupling; 6.3 Applications.
Summary This book provides the basis of a formal language and explores its possibilities in the characterization of multiplex networks. Armed with the formalism developed, the authors define structural metrics for multiplex networks. A methodology to generalize monoplex structural metrics to multiplex networks is also presented so that the reader will be able to generalize other metrics of interest in a systematic way. Therefore, this book will serve as a guide for the theoretical development of new multiplex metrics. Furthermore, this Brief describes the spectral properties of these networks in relation to concepts from algebraic graph theory and the theory of matrix polynomials. The text is rounded off by analyzing the different structural transitions present in multiplex systems as well as by a brief overview of some representative dynamical processes. Multiplex Networks will appeal to students, researchers, and professionals within the fields of network science, graph theory, and data science.
Other author Arruda, Guilherme Ferraz de, author.
Rodrigues, Francisco Aparecido, author.
Moreno, Yamir, author.
SpringerLink issuing body.
Subject System analysis.
Graph theory.
Electronic books.
ISBN 9783319922553 (electronic bk.)
3319922556 (electronic bk.)
Standard Number 10.1007/978-3-319-92255-3