Spectral graph analysis of modularity and assortativity

被引：38
|
作者：
Van Mieghem, P. [1 ]
Ge, X. [2 ]
Schumm, P. [3 ]
Trajanovski, S. [1 ]
Wang, H. [1 ]
机构：
[1] Delft Univ Technol, Fac Elect Engn Math & Comp Sci, NL-2600 GA Delft, Netherlands
[2] Northeastern Univ, Coll Informat Sci & Engn, Shenyang 110004, Peoples R China
[3] Kansas State Univ, Dept Elect & Comp Engn, Manhattan, KS 66506 USA
来源：
PHYSICAL REVIEW E | 2010年 / 82卷 / 05期
关键词：
RESOLUTION;
D O I：
10.1103/PhysRevE.82.056113
中图分类号：
O35 [流体力学]; O53 [等离子体物理学];
学科分类号：
070204 ; 080103 ; 080704 ;
摘要：
Expressions and bounds for Newman's modularity are presented. These results reveal conditions for or properties of the maximum modularity of a network. The influence of the spectrum of the modularity matrix on the maximum modularity is discussed. The second part of the paper investigates how the maximum modularity, the number of clusters, and the hop count of the shortest paths vary when the assortativity of the graph is changed via degree-preserving rewiring. Via simulations, we show that the maximum modularity increases, the number of clusters decreases, and the average hop count and the effective graph resistance increase with increasing assortativity.
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收藏
页数：11
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