Paper Info
Title
Extended corona product as an exactly tractable model for weighted heterogeneous networks.
Abstract
Various graph products and operations have been widely used to construct complex networks with common properties of real-life systems. However, current works mainly focus on designing models of binary networks, in spite of the fact that many real networks can be better mimicked by heterogeneous weighted networks. In this paper, we develop a corona product of two weighted graphs, based on which and an observed updating mechanism of edge weight in real networks, we propose a minimal generative model for inhomogeneous weighted networks. We derive analytically relevant properties of the weighted network model, including strength, weight and degree distributions, clustering coefficient, degree correlations and diameter. These properties are in good agreement with those observed in diverse real-world weighted networks. We then determine all the eigenvalues and their corresponding multiplicities of the transition probability matrix for random walks on the weighted networks. Finally, we apply the obtained spectra to derive explicit expressions for mean hitting time of random walks and weighted counting of spanning trees on the weighted networks. Our model is an exactly solvable one, allowing us to analytically treat its structural and dynamical properties, which is thus a good test-bed and an ideal substrate network for studying different dynamical processes, in order to explore the impacts of heterogeneous weight distribution on these processes.
Year
DOI
Venue
2018
10.1093/comjnl/bxx094
COMPUTER JOURNAL
Keywords
DocType
Volume
graph product,corona product,weighted complex network,random walk,graph spectra,weighted spanning trees
Journal
61
Issue
ISSN
Citations 
5
0010-4620
3
PageRank 
References 
Authors
0.38
14
3
Name
Order
Citations
PageRank
Yi Qi182.14
Huan Li2184.60
Zhongzhi Zhang38522.02