Abstract
We come up with a punishment in the form of exponential decay for the number of vertices that a path passes through, which is able to reconcile the contradictory effects of geodesic length and edge weights. This core thought is the key to handling three typical applications; that is, given an information demander, he may be faced with the following problems: choosing optimal route to contact the single supplier, picking out the best supplier between multiple candidates, and calculating his point centrality, which involves indirect connections. Accordingly, three concrete solutions in one logic thread are proposed. Firstly, by adding a constraint to Dijkstra algorithm, we limit our candidates for optimal route to the sample space of geodesics. Secondly, we come up with a unified standard for the comparison between adjacent and nonadjacent vertices. Through punishment in the form of exponential decay, the attenuation effect caused by the number of vertices that a path passes through has been offset. Then the adjacent vertices and punished nonadjacent vertices can be compared directly. At last, an unprecedented centrality index, quasi-closeness, is ready to come out, with direct and indirect connections being summed up.
Highlights
Among many social network analysis (SNA) methods, point centrality has received particular focus from network researchers
We propose a quasi-closeness centrality index which is capable of being applied for valued graphs
We propose an unprecedented centrality index that takes into account both direct and indirect connections
Summary
Among many social network analysis (SNA) methods, point centrality has received particular focus from network researchers. Mathematical Problems in Engineering fades with distance Following this thread, many centrality indexes based on shortest path are proposed by researchers. Given a pair of unordered vertices in an undirected valued graph, the optimal path for information spreading or communication must be a geodesic. This premise is born from the idea that information attenuation caused by longer distance is serious enough to neutralize the information augment arising from more weight. We set penalty in form of exponential decay for geodesics distance, and the decay indices are flexible values depending on concrete applications This unified standard can be applied to find the optimal partner in a network.
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