Multiplex networks : basic formalism and structural properties /: basic formalism and structural properties. ([2018])

• Record Type: Book
• Further Information: Note: Emanuele Cozzo, Guilherme Ferraz de Arruda, Francisco Aparecido Rodrigues, Yamir Moreno.
• Authors: Cozzo, Emanuele; Arruda, Guilherme Ferraz de; Rodrigues, Francisco Aparecido; Moreno, Yamir
• 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; 2.3.1.1 Adjacency and Laplacian Matrices; 2.3.1.2 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. 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource, illustrations
• Subjects: 003; Physics; System analysis; Graph theory; Matrices; SCIENCE -- System Theory; TECHNOLOGY & ENGINEERING -- Operations Research; Graph theory; Matrices; System analysis; Mathematics -- Graphic Methods; Business & Economics -- Industries -- Computer Industry; Combinatorics & graph theory; Business mathematics & systems; Big data; Mathematical physics; Electronic books
• Languages: English
• ISBNs: 9783319922553; 3319922556
• Related ISBNs: 9783319922546; 3319922548
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed July 03, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.