Directed Random Dot Product Graphs

In this paper we consider three models for random graphs that utilize the inner product as their fundamental object. We analyze the behavior of these models with respect to clustering, the small world property, and degree distribution. These models are motivated by the random dot product graphs developed by Kraetzl, Nickel and Scheinerman. We extend their results to fully parameterize the conditions under which clustering occurs, characterize the diameter of graphs generated by these models, and describe the behavior of the degree distribution. With the ubiquity and importance of the Internet and genetic information in medicine and biology, the study of complex networks relating to the Internet and genetics continues to be an important and vital area of study. This is especially true for networks such as the physical layer of the Internet, the link structure of the world wide web, and protein-protein and protein-gene interaction networks. Because of the size of these networks [3] and t...

• Type: Journal
• Year: 2008
• Where: IM
• Authors: Stephen J. Young, Edward R. Scheinerman
• Keywords: Complex Networks, IM 2007, IM 2008, Random Dot Product, Small World Property