Analysis of topology dynamics for unstructured P2P networks

In this paper, we propose an evolution model for unstructured Peer-to-Peer (P2P) file-sharing systems, which tries to capture the dynamic properties of P2P application networks. The model consists of four most important events in the evolution of network topology: node addition, node departure, connection establishment, and edge deletion. Based on the model, we derive a difference equation of degree distribution, which can be solved analytically. By analyzing the solutions, we find that there are two factors affecting the degree distribution. The first one represents the internal dynamics of network topology, while the second one represents the external influence. We find that the internal dynamics makes the degree distribution follow power law while the external influence makes it deviate from power law. User behaviors and resource distributions are the main reasons for this deviation.