Eccentricities on small-world networks

This paper focuses on the efficiency issue of computing and maintaining the eccentricity distribution on a large and perhaps dynamic small-world network. Eccentricity distribution evaluates the importance of each node in a graph, providing a node ranking for graph analytics; moreover, it is the key to the computation of two fundamental graph measurements, diameter, and radius. Existing eccentricity computation algorithms are not scalable enough to handle real large networks unless approximation is introduced. Such an approximation, however, leads to a prominent relative error on small-world networks whose diameters are notably short. Our solution optimizes existing eccentricity computation algorithms on their bottlenecks—one-node eccentricity computation and the upper/lower bounds update—based on a line of original insights; it also provides the first algorithm on maintaining the eccentricities of a dynamic graph without recomputing the eccentricity distribution upon each edge update. On real large small-world networks, our approach outperforms the state-of-the-art eccentricity computation approach by up to three orders of magnitude and our maintenance algorithm outperforms the recomputation baseline (recompute using our superior eccentricity computation approach) by up to two orders of magnitude, as demonstrated by our extensive evaluation.