Distributed Current Flow Betweeness Centrality

—The computation of nodes centrality is of great importance for the analysis of graphs. The current flow betweenness is an interesting centrality index that is computed by considering how the information travels along all the possible paths of a graph. The current flow betweenness exploits basic results from electrical circuits, i.e. Kirchhoff’s laws, to evaluate the centrality of vertices. The computation of the current flow betweenness may exceed the computational capability of a single machine for very large graphs composed by millions of nodes. In this paper we propose a solution that estimates the current flow betweenness in a distributed setting, by defining a vertex-centric, gossip-based algorithm. Each node, relying on its local information, in a selfadaptive way generates new flows to improve the betweenness of all the nodes of the graph. Our experimental evaluation shows that our proposal achieves high correlation with the exact current flow betweenness, and provides a good centrality measure for large graphs

A variant of the current flow betweenness centrality and its application in urban networks

The current flow betweenness centrality is a useful tool to estimate traffic status in spatial networks and, in general, to measure the intermediation of nodes in networks where the transition between them takes place in a random way. The main drawback of this centrality is its high computational cost, especially for very large networks, as it is the case of urban networks. In this paper, a new approach to the current flow betweenness centrality for its practical application in urban networks with data is presented and discussed. The new centrality measure allows the estimation of pedestrian flow developed in urban networks, taking into account both the network topology and its associated data. In addition, its computational cost makes it suitable for application in networks with a large number of nodes. Some examples are studied in order to better understand the characteristics and behaviour of the proposed centrality in the context of the city.Partially supported by the Spanish Government, Ministerio de Economía y Competividad, grant number TIN2017-84821-P

The Power of Quasi-Shortest Paths: ρ-Geodesic Betweenness Centrality

International audienceBetweenness centrality metrics usually underestimate the importance of nodes that are close to shortest paths but do not exactly fall on them. In this paper, we reevaluate the importance of such nodes and propose the ρ-geodesic betweenness centrality, a novel metric that assigns weights to paths (and, consequently, to nodes on these paths) according to how close they are to shortest paths. The paths that are just slightly longer than the shortest one are defined as quasi-shortest paths, and they are able to increase or to decrease the importance of a node according to how often the node falls on them. We compare the proposed metric with the traditional, distance-scaled, and random walk betweenness centralities using four network datasets with distinct characteristics. The results show that the proposed metric, besides better assessing the topological role of a node, is also able to maintain the rank position of nodes overtime compared to the other metrics; this means that network dynamics affect less our metric than others. Such a property could help avoid, for instance, the waste of resources caused when data follow only the shortest paths and reduce associated costs