Detecting communities via edge Random Walk Centrality

Herein we present a novel approach of identifying community structures in complex networks. We propose the usage of the Random Walk Centrality (RWC), first introduced by Noh and Rieger [Phys. Rev. Lett. 92.11 (2004): 118701]. We adapt this node centrality metric to an edge centrality metric by applying it to the line graph of a given network. A crucial feature of our algorithm is the needlessness of recalculating the centrality metric after each step, in contrast to most community detection algorithms. We test our algorithm on a wide variety of standard networks, and compare them with pre-existing algorithms. As a predictive application, we analyze the Indian Railway network for robustness and connectedness, and propose edges which would make the system even sturdier.Comment: 12 pages, 8 figure

Novel Edge and Density Metrics for Link Cohesion

We present a new metric of link cohesion for measuring the strength of edges in complex, highly connected graphs. Link cohesion accounts for local small hop connections and associated node degrees and can be used to support edge scoring and graph simplification. We also present a novel graph density measure to estimate the average cohesion across nodes. Link cohesion and the density measure are employed to demonstrate community detection through graph sparsification by maximizing graph density. Link cohesion is also shown to be loosely correlated with edge betweenness centrality

Centrality Metric for Dynamic Networks

Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to static networks. Most networks, on the other hand, are dynamic in nature, evolving over time through the addition or deletion of nodes and edges. A popular approach to analyzing such networks represents them by a static network that aggregates all edges observed over some time period. This approach, however, under or overestimates centrality of some nodes. We address this problem by introducing a novel centrality metric for dynamic network analysis. This metric exploits an intuition that in order for one node in a dynamic network to influence another over some period of time, there must exist a path that connects the source and destination nodes through intermediaries at different times. We demonstrate on an example network that the proposed metric leads to a very different ranking than analysis of an equivalent static network. We use dynamic centrality to study a dynamic citations network and contrast results to those reached by static network analysis.Comment: in KDD workshop on Mining and Learning in Graphs (MLG

Offloading Content with Self-organizing Mobile Fogs

Mobile users in an urban environment access content on the internet from different locations. It is challenging for the current service providers to cope with the increasing content demand from a large number of collocated mobile users. In-network caching to offload content at nodes closer to users alleviate the issue, though efficient cache management is required to find out who should cache what, when and where in an urban environment, given nodes limited computing, communication and caching resources. To address this, we first define a novel relation between content popularity and availability in the network and investigate a node's eligibility to cache content based on its urban reachability. We then allow nodes to self-organize into mobile fogs to increase the distributed cache and maximize content availability in a cost-effective manner. However, to cater rational nodes, we propose a coalition game for the nodes to offer a maximum "virtual cache" assuming a monetary reward is paid to them by the service/content provider. Nodes are allowed to merge into different spatio-temporal coalitions in order to increase the distributed cache size at the network edge. Results obtained through simulations using realistic urban mobility trace validate the performance of our caching system showing a ratio of 60-85% of cache hits compared to the 30-40% obtained by the existing schemes and 10% in case of no coalition

Numerical Investigation of Metrics for Epidemic Processes on Graphs

This study develops the epidemic hitting time (EHT) metric on graphs measuring the expected time an epidemic starting at node $a$ in a fully susceptible network takes to propagate and reach node $b$. An associated EHT centrality measure is then compared to degree, betweenness, spectral, and effective resistance centrality measures through exhaustive numerical simulations on several real-world network data-sets. We find two surprising observations: first, EHT centrality is highly correlated with effective resistance centrality; second, the EHT centrality measure is much more delocalized compared to degree and spectral centrality, highlighting the role of peripheral nodes in epidemic spreading on graphs.Comment: 6 pages, 1 figure, 3 tables, In Proceedings of 2015 Asilomar Conference on Signals, Systems, and Computer