| Full text | |
| Author(s): |
Ye, Cheng
;
Wilson, Richard C.
;
Comin, Cesar H.
;
Costa, Luciano da F.
;
Hancock, Edwin R.
Total Authors: 5
|
| Document type: | Journal article |
| Source: | PHYSICAL REVIEW E; v. 89, n. 5, p. 12-pg., 2014-05-12. |
| Abstract | |
In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks. (AU) | |
| FAPESP's process: | 11/22639-8 - Unveiling the relationship between structure and dynamics on modular networks |
| Grantee: | Cesar Henrique Comin |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 11/50761-2 - Models and methods of e-Science for life and agricultural sciences |
| Grantee: | Roberto Marcondes Cesar Junior |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 12/50986-7 - Graph spectra and complex network evolution |
| Grantee: | Luciano da Fontoura Costa |
| Support Opportunities: | Regular Research Grants |