Modeling Peer-to-peer Network Topologies through “small-world” Models and Power Laws

I INTRODUCTION The recent emergence of novel network applications such as Gnutella, Freenet, and Napster has reincarnated the familiar peer-to-peer (P2P) architecture model of the original Internet in new and innovative ways in an effort to facilitate worldwide sharing of information [1]. As a result, there is an ever-increasing need for distributed protocols that would allow peer-to-peer applications to scale to a large community of users. The main difficulty in designing such protocols is that currently, very little is known about the nature of networks on which they would be operating. Current protocols were designed without any knowledge about the underlying network topology. The end result is that even simple protocols, as in the case of Gnutella, result in complex interactions that can adversely affect system performance. To study these interactions, we first need an accurate model of the network topology. We model the topology of P2P networks by undirected graph G, where nodes represent hosts and edges represent connections between those hosts. In this paper we point out several important structural characteristics of the P2P network topology graph, namely the " small-world " properties and several power law distributions of various graph metrics. We report measurements through experimental studies of a large P2P network application known as Gnutella. To obtain the Gnutella topology data, a network crawler that allows topology discovery to be performed in parallel was developed. Upon analysing the obtained topology data, we discovered it exhibits strong "small-world" properties. More specifically, the properties of small diameter and clustering were observed. In addition, we report evidence of four different power laws previously observed in other technological networks, such as the Internet and the WWW. Recent research results show that the " small-world " and power-law properties of the underlying network topology can significantly impact the performance of algorithms such as those for routing and searching [2, 3]. Therefore the existence of these properties in P2P networks presents an important issue to consider when designing new, more-scalable application-level protocols. II " SMALL-WORLD " PROPERTIES The term " small-world " originated with a famous social experiment conducted by Stanley Milgram in the late 1960s. Watts and Strogatz in [4] showed that other networks, such as those occurring in nature and technology, also exhibit "small-world" behavior. Throughout this work we use the term " small-world " loosely to mean that the network possesses both small diameter and is also highly clustered. …