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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 7420281, 9 pages
Research Article

Quasi-Closeness: A Toolkit for Social Network Applications Involving Indirect Connections

School of Securities and Futures, Southwestern University of Finance and Economics, Chengdu, China

Correspondence should be addressed to Yahui Liu

Received 11 March 2017; Accepted 11 May 2017; Published 6 August 2017

Academic Editor: Yakov Strelniker

Copyright © 2017 Yugang Yin and Yahui Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.