This paper proposes a new measure of node centrality in social networks, the Harmonic Influence Centrality, which emerges naturally in the study of social influence over networks. Using an intuitive analogy between social and electrical networks, we introduce a distributed message passing algorithm to compute the Harmonic Influence Centrality of each node. Although its design is based on theoretical results which assume the network to have no cycle, the algorithm can also be successfully applied on general graphs.
As opposed to centralized algorithms, the interest for distributed algorithms to compute centrality measures has risen more recently. @cite_8 a randomized algorithm is used to compute PageRank centrality. @cite_12 distributed algorithms are designed to compute node (and edge) betweenness on trees, but are not suitable for general graphs.
@cite_12 @cite_8
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This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, κ-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high κ-path centrality have high node betweenness centrality. The randomized algorithm runs in time O(κ3n2−2αlog n) and outputs, for each vertex v, an estimate of its κ-path centrality up to additive error of ±n1 2+α with probability 1 − 1 n2. Experimental evaluations on real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared with existing randomized algorithms. Betweenness centrality is a fundamental measure in social network analysis, expressing the importance or influence of individual vertices (or edges) in a network in terms of the fraction of shortest paths that pass through them. Since exact computation in large networks is prohibitively expensive, we present two efficient randomized algorithms for betweenness estimation. The algorithms are based on random sampling of shortest paths and offer probabilistic guarantees on the quality of the approximation. The first algorithm estimates the betweenness of all vertices (or edges): all approximate values are within an additive factor @math ??(0,1) from the real values, with probability at least @math 1-?. The second algorithm focuses on the top-K vertices (or edges) with highest betweenness and estimate their betweenness value to within a multiplicative factor @math ?, with probability at least @math 1-?. This is the first algorithm that can compute such approximation for the top-K vertices (or edges). By proving upper and lower bounds to the VC-dimension of a range set associated with the problem at hand, we can bound the sample size needed to achieve the desired approximations. We obtain sample sizes that are independent from the number of vertices in the network and only depend on a characteristic quantity that we call the vertex-diameter, that is the maximum number of vertices in a shortest path. In some cases, the sample size is completely independent from any quantitative property of the graph. An extensive experimental evaluation on real and artificial networks shows that our algorithms are significantly faster and much more scalable as the number of vertices grows than other algorithms with similar approximation guarantees. In this paper, we describe a new distributed community detection algorithm for billion-edge directed graphs that, unlike modularity-based methods, achieves cluster quality on par with the best-known algorithms in the literature. We show that a simple approximation to the best-known serial algorithm dramatically reduces computation and enables distributed evaluation yet incurs only a very small impact on cluster quality. We present three main results: First, we show that the clustering produced by our scalable approximate algorithm compares favorably with prior results on small synthetic benchmarks and small real-world datasets (70 million edges). Second, we evaluate our algorithm on billion-edge directed graphs (a 1.5B edge social network graph, and a 3.7B edge web crawl), and show that the results exhibit the structural properties predicted by analysis of much smaller graphs from similar sources. Third, we show that our algorithm exhibits over 90 parallel efficiency on massive graphs in weak scaling experiments. Centrality measures are used in network science to rank the relative importance of nodes and edges of a graph. Here we define new measures of centrality for power grid structure that are based on its functionality. We show that the relative importance analysis based on centrality in graph theory can be generalized to power grid network with its electrical parameters taken into account. In the paper we experiment with the proposed electrical centrality measures on the NYISO-2935 system and the IEEE 300-bus system. We analyze the centrality distribution in order to identify important nodes or branches in the system which are of essential importance in terms of system vulnerability. We also present and discuss a number of interesting discoveries regarding the importance rank of power grid nodes and branches.