Graph Theoretical Analysis on Distributed Line Graphs for Peer-to-Peer Networks

Distributed line graphs were introduced by Zhang and Liu as an overlay for Peer-to-Peer networks. Distributed line graphs have some useful properties as a network topology, such as out-regular and small diameter, where the former implies that each user possesses a constant size of routing table and the latter means that a reasonably small number of hops is necessary to reach a target user. In this paper, we newly introduce distributed line sharp graphs, as an extension of distributed line graphs, so as to further expand the possibility of finding better network topologies and theoretically analyze their properties. The analysis on the distributed line sharp graphs is based on the analysis on distributed line graphs presented by Zhang and Liu. In particular, we further examine the diameter and the in-degree of a vertex, and improve the previous results together with detailed proofs. We also show that the diameter of a certain distributed line sharp graph is equal to the diameter of its corresponding distributed line graph.