AIMR Math Group On-line Seminar

#2 FY2021

 

Date : April. 30th (Fri) 2021 10:00–11:00

Venue: Zoom

Speaker: Yuka Fujiki (WPI-AIMR, Tohoku University)
Title: A framework for analyzing long-range degree correlations in complex networks

 

Abstract

A network representation is one of the most efficient ways to abstract pairwise interaction in real-world complex systems. In many complex networks, the number of edges from a node, namely degree, widely fluctuates from node to node, and the broad distribution of degrees indicates the importance of degree-degree correlations. In particular, correlations between degrees of adjacent nodes, that is, nearest neighbor degree correlations (NNDCs) are deeply related to fundamental properties of network structures and influence various dynamics on networks. However, NNDCs are not enough to characterize network structures. The shortest path distance between hub nodes influences many structural and/or dynamical properties of networks. For understanding these properties systematically, we provide a general framework to analyze long-range degree correlations (LRDCs) between nodes separated by more than one step. The presented method is based on the joint and conditional probability distributions describing LRDC. To detect the existence of LRDC in a given network G, we analytically calculate the probability distributions for random networks with the same degree distribution as G within a mean-field approximation. Although most real-world networks are revealed to exhibit LRDCs by applying our method to them, we should note that NNDCs induce LRDCs extrinsically. In order to distinguish such extrinsic LRDCs and intrinsic LRDCs that cannot be produced by NNDCs, we employ nearest-neighbor correlated random networks (NNCRNs) and analytically calculate the probability distributions for them. Intrinsic LRDC in a given network can be identified by comparing its probability distributions with those for NNCRNs.

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