Routing betweenness centrality

Abstract

Betweenness-Centrality measure is often used in social and computer communication networks to estimate the potential monitoring and control capabilities a vertex may have on data flowing in the network. In this article, we define the Routing Betweenness Centrality (RBC) measure that generalizes previously well known Betweenness measures such as the Shortest Path Betweenness, Flow Betweenness, and Traffic Load Centrality by considering network flows created by arbitrary loop-free routing strategies.We present algorithms for computing RBC of all the individual vertices in the network and algorithms for computing the RBC of a given group of vertices, where the RBC of a group of vertices represents their potential to collaboratively monitor and control data flows in the network. Two types of collaborations are considered: (i) conjunctive-the group is a sequences of vertices controlling traffic where all members of the sequence process the traffic in the order defined by the sequence and (ii) disjunctive-the group is a set of vertices controlling traffic where at least one member of the set processes the traffic. The algorithms presented in this paper also take into consideration different sampling rates of network monitors, accommodate arbitrary communication patterns between the vertices (traffic matrices), and can be applied to groups consisting of vertices and/or edges.For the cases of routing strategies that depend on both the source and the target of the message, we present algorithms with time complexity of O(n 2 m) where n is the number of vertices in the network and m is the number of edges in the routing tree (or the routing directed acyclic graph (DAG) for the cases of multi-path routing strategies). The time complexity can be reduced by an order of n if we assume that the routing decisions depend solely on the target of the messages.Finally, we show that a preprocessing of O(n 2 m) time, supports computations of RBC of sequences in O(kn) time and computations of RBC of sets in O(k 3 n) time, where k in the number of vertices in the sequence or the set.

Augmented Betweenness Centrality for Environmentally Aware Traffic Monitoring in Transportation Networks

“…Although the first was thoroughly studied in the previous sections, analyzing the effect of the sampling rate over the performance of the system is a much simpler task (Dolev et al, 2010). With low sampling rates, GBC becomes proportional to the sum of BC values of the group members (as the number of redundant inspections reduces with the sampling rate).…”

“…Let σ s,t be the number of shortest paths between the origin vertex s ∈ V and the destination vertex t ∈ V . Some variants of Betweenness relieve the shortest path constraint allowing deviations from the minimal distance between the two vertices (Dolev et al, 2010) or even equally considering all paths or random walks (Freeman et al, 1991;Newman, 2005). In the rest of this article we will refer to the shortest or "almost" shortest paths between two vertices as routes.…”

Fast approximation of betweenness centrality through sampling

“…This is not to be confused with "k-path betweenness centrality" (Kourtellis et al 2012), which considers simple random walks that are not necessarily shortest paths. Dolev et al (2010) present a generalization of betweenness centrality which takes into account routing policies in the network. Opsahl et al (2010) define a new distance function between pair of vertices in order to penalize paths with a high number of hops in weighted network.…”

The Power of Quasi-Shortest Paths: $\rho$ -Geodesic Betweenness Centrality

“…It is known that network protocols can greatly benefit from this metric [12], [13], [14], [15]. We argue, however, that using only such paths to assign importance to a node may underestimate other important nodes -in particular, those in the close vicinity of shortest paths but that do not belong to them.…”