Community is an important attribute of Pocket Switched Networks (PSN), because mobile devices are carried by people who tend to belong to communities. We analysed community structure from mobility traces and used for forwarding algorithms [12], which shows significant impact of community. Here, we propose and evaluate three novel distributed community detection approaches with great potential to detect both static and temporal communities. We find that with suitable configuration of the threshold values, the distributed community detection can approximate their corresponding centralised methods up to 90% accuracy.

Two problems are considered in the present paper as examples of the integral method formulated in part I (the preceding paper). The first concerns arcs in uniform flow, and it is shown that the only form of steady solution, if the conductance shape factor is taken to be a function of power level, is the fully developed arc. A known solution of the full differential equations provides a test of the adequacy of the result. Free recovery is briefly discussed. The second problem concerns steady arcs in nozzles. With the assumptions of constant shape factors and negligible radiation, a simple model is derived which provides insight into behaviour as a nozzle-blocking condition is approached.

Measuring the centrality of nodes in real-world networks has remained an important task in the technological, social, and biological network paradigms carrying implications on their analysis and applications. Exact inference of centrality values is infeasible in large networks due to the need to solve the all-pairs shortest path problem. We introduce a framework to approximate node centralities in real-world networks that are known to exhibit modularity, i.e., the presence of dense subgraphs or communities, which are themselves sparsely connected. We also propose a novel centrality measure known as Community Inbetweenness that ranks nodes based solely on community information. In a modular network of size n with √ n evenly sized communities and m edges, our framework requires linear time O(m) and O( √ nm) time for the approximation of closeness and betweenness respectively. Utilizing a recently proposed linear time method in community detection, our approximation techniques are faster than traditional sampling algorithms, applicable in real-time distributed environments, and offer highly comparable results. Figure 1: The snapshot of a 500-node subgraph of the Orkut OSN reveals clear modular structure. The size of the nodes corresponds to their betweenness centrality.

Abstract. In this paper, we present our ongoing work on developing a framework for detecting time-varying communities on human mobile networks. We define the term community in environments where the mobility patterns and clustering behaviors of individuals vary in time. This work provides a method to describe, analyze, and compare the clustering behaviors of collections of mobile entities, and how they evolve over time.

For pt.II see ibid., vol.7, p.2232 (1974). The energy equation for the core of axisymmetric electric arcs is de- rived in terms of radial integrals. The formulation includes terms to describe the diffusive heat flux at the core boundary and the work done against viscous stress there. When the shape factors derived in Part I are evaluated for a number of different arc situations from known differential solutions, they correlate well in terms of a non-dimensional form of the heat flux. This result suggests that arc behaviour can be predicted accurately by the overall integral equations of Part I and the core energy equation, together with empirical curves relating shape factors to non-dimensional heat flux, provided that the flow is laminar and there is negligible radiation.