Spectra of random networks in the weak clustering regime

The asymptotic behavior of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these mo...

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Bibliographic Details
Published in:Europhysics letters 2018-03, Vol.121 (6), p.68001, Article 68001
Main Authors: Peron, Thomas K. DM, Ji, Peng, Kurths, Jürgen, Rodrigues, Francisco A.
Format: Article
Language:English
Subjects:
02.70.Hm
64.60.aq
89.75.Hc
Asymptotic properties
Clustering
Dynamic structural analysis
Graph theory
Matrix theory
Modular structures
Networks
Spectra
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Summary:The asymptotic behavior of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these models fail to describe many topological features of real-world networks, in particular non-null values of the clustering coefficient. Here we study effects of cycles of order three (triangles) in network spectra. By using recent advances in random matrix theory, we determine the spectral distribution of the network adjacency matrix as a function of the average number of triangles attached to each node for networks without modular structure and degree-degree correlations. Implications to network dynamics are discussed. Our findings can shed light in the study of how particular kinds of subgraphs influence network dynamics.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/121/68001