668 research outputs found
Triadic Measures on Graphs: The Power of Wedge Sampling
Graphs are used to model interactions in a variety of contexts, and there is
a growing need to quickly assess the structure of a graph. Some of the most
useful graph metrics, especially those measuring social cohesion, are based on
triangles. Despite the importance of these triadic measures, associated
algorithms can be extremely expensive. We propose a new method based on wedge
sampling. This versatile technique allows for the fast and accurate
approximation of all current variants of clustering coefficients and enables
rapid uniform sampling of the triangles of a graph. Our methods come with
provable and practical time-approximation tradeoffs for all computations. We
provide extensive results that show our methods are orders of magnitude faster
than the state-of-the-art, while providing nearly the accuracy of full
enumeration. Our results will enable more wide-scale adoption of triadic
measures for analysis of extremely large graphs, as demonstrated on several
real-world examples
Efficient computation of the Weighted Clustering Coefficient
The clustering coefficient of an unweighted network has been extensively used to quantify how tightly connected is the neighbor around a node and it has been widely adopted for assessing the quality of nodes in a social network. The computation of the clustering coefficient is challenging since it requires to count the number of triangles in the graph. Several recent works proposed efficient sampling, streaming and MapReduce algorithms that allow to overcome this computational bottleneck. As a matter of fact, the intensity of the interaction between nodes, that is usually represented with weights on the edges of the graph, is also an important measure of the statistical cohesiveness of a network. Recently various notions of weighted clustering coefficient have been proposed but all those techniques are hard to implement on large-scale graphs. In this work we show how standard sampling techniques can be used to obtain efficient estimators for the most commonly used measures of weighted clustering coefficient. Furthermore we also propose a novel graph-theoretic notion of clustering coefficient in weighted networks. © 2016, Copyright © Taylor & Francis Group, LL
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