Corrected Overlap Weight and Clustering Coefficient

Abstract

Copyright © 2019, arXiv, All rights reserved. We discuss two well known network measures: The overlap weight of an edge and the clustering coefficient of a node. For both of them it turns out that they are not very useful for data analytic task to identify important elements (nodes or links) of a given network. The reason for this is that they attain their largest values on maximal subgraphs of relatively small size that are more probable to appear in a network than that of larger size. We show how the definitions of these measures can be corrected in such a way that they give the expected results. We illustrate the proposed corrected measures by applying them on the US Airports network using the program Pajek.MSC Codes 91D30, 91C05, 05C85, 68R10, 05C42