Fast Multi-Scale Community Detection based on Local Criteria within a Multi-Threaded Algorithm

Many systems can be described using graphs, or networks. Detecting communities in these networks can provide information about the underlying structure and functioning of the original systems. Yet this detection is a complex task and a large amount of work was dedicated to it in the past decade. One important feature is that communities can be found at several scales, or levels of resolution, indicating several levels of organisations. Therefore solutions to the community structure may not be unique. Also networks tend to be large and hence require efficient processing. In this work, we present a new algorithm for the fast detection of communities across scales using a local criterion. We exploit the local aspect of the criterion to enable parallel computation and improve the algorithm's efficiency further. The algorithm is tested against large generated multi-scale networks and experiments demonstrate its efficiency and accuracy.Comment: arXiv admin note: text overlap with arXiv:1204.100

Uncovering nodes that spread information between communities in social networks

From many datasets gathered in online social networks, well defined community structures have been observed. A large number of users participate in these networks and the size of the resulting graphs poses computational challenges. There is a particular demand in identifying the nodes responsible for information flow between communities; for example, in temporal Twitter networks edges between communities play a key role in propagating spikes of activity when the connectivity between communities is sparse and few edges exist between different clusters of nodes. The new algorithm proposed here is aimed at revealing these key connections by measuring a node's vicinity to nodes of another community. We look at the nodes which have edges in more than one community and the locality of nodes around them which influence the information received and broadcasted to them. The method relies on independent random walks of a chosen fixed number of steps, originating from nodes with edges in more than one community. For the large networks that we have in mind, existing measures such as betweenness centrality are difficult to compute, even with recent methods that approximate the large number of operations required. We therefore design an algorithm that scales up to the demand of current big data requirements and has the ability to harness parallel processing capabilities. The new algorithm is illustrated on synthetic data, where results can be judged carefully, and also on a real, large scale Twitter activity data, where new insights can be gained

Centrality Measures for Networks with Community Structure

Understanding the network structure, and finding out the influential nodes is a challenging issue in the large networks. Identifying the most influential nodes in the network can be useful in many applications like immunization of nodes in case of epidemic spreading, during intentional attacks on complex networks. A lot of research is done to devise centrality measures which could efficiently identify the most influential nodes in the network. There are two major approaches to the problem: On one hand, deterministic strategies that exploit knowledge about the overall network topology in order to find the influential nodes, while on the other end, random strategies are completely agnostic about the network structure. Centrality measures that can deal with a limited knowledge of the network structure are required. Indeed, in practice, information about the global structure of the overall network is rarely available or hard to acquire. Even if available, the structure of the network might be too large that it is too much computationally expensive to calculate global centrality measures. To that end, a centrality measure is proposed that requires information only at the community level to identify the influential nodes in the network. Indeed, most of the real-world networks exhibit a community structure that can be exploited efficiently to discover the influential nodes. We performed a comparative evaluation of prominent global deterministic strategies together with stochastic strategies with an available and the proposed deterministic community-based strategy. Effectiveness of the proposed method is evaluated by performing experiments on synthetic and real-world networks with community structure in the case of immunization of nodes for epidemic control.Comment: 30 pages, 4 figures. Accepted for publication in Physica A. arXiv admin note: text overlap with arXiv:1411.627