On random walks in direction-aware network problems

Graph theory provides a powerful set of metrics and conceptual ideas to model and investigate the behavior of communication networks. Most graph-theoretical frameworks in the networking literature are based on undirected graph models, where a symmetric link weight is assigned to each link of the network. However, many communication networks must account for directionality of communication links. This paper reports on an effort to extend some of the existing results of symmetric graphs to asymmetric ones. In particular we are interested in the behavior of random-walk based algorithms in directed graphs and we find the average travel time of a random-walk as a function of an asymmetric Laplacian matrix, which is in turn a function of link weights.

• Type: Journal
• Year: 2010
• Where: SIGMETRICS
• Authors: Ali Tizghadam, Alberto Leon-Garcia
• Keywords: Hardware, Link Weights, SIGMETRICS 2010, Symmetric Link Weight, Undirected Graph Models