Paper Info
Title
A Generalized Configuration Model with Degree Correlations and Its Percolation Analysis
Abstract
In this paper we present a generalization of the classical configuration model. Like the classical configuration model, the generalized configuration model allows users to specify an arbitrary degree distribution. In our generalized configuration model, we partition the stubs in the configuration model into b blocks of equal sizes and choose a permutation function h for these blocks. In each block, we randomly designate a number proportional to q of stubs as type 1 stubs, where q is a parameter in the range [0,1]. Other stubs are designated as type 2 stubs. To construct a network, randomly select an unconnected stub. Suppose that this stub is in block i. If it is a type 1 stub, connect this stub to a randomly selected unconnected type 1 stub in block h(i). If it is a type 2 stub, connect it to a randomly selected unconnected type 2 stub. We repeat this process until all stubs are connected. Under an assumption, we derive a closed form for the joint degree distribution of two random neighboring vertices in the constructed graph. Based on this joint degree distribution, we show that the Pearson degree correlation function is linear in q for any fixed b. By properly choosing h, we show that our construction algorithm can create assortative networks as well as disassortative networks. We present a percolation analysis of this model. We verify our results by extensive computer simulations.
Year
DOI
Venue
2019
10.1007/s41109-019-0240-2
Applied Network Science
Keywords
DocType
Volume
Configuration model, Assortative mixing, Degree correlation
Journal
4
Issue
ISSN
Citations 
1
2364-8228
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Duan-Shin Lee167071.00
Cheng-Shang Chang22392246.97
Zhu Miao300.34
Li Hung-Chih400.34