Abstract
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 to the US Airports network using the program Pajek.
Mathematics Subject Classification 2010: 91D30, 91C05, 05C85, 68R10, 05C42
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Acknowledgements
The computations were done combining Pajek [11] with short programs in Python and R [12].
This work is supported in part by the Slovenian Research Agency (research program P1-0294 and research projects J1-9187 and J7-8279) and by Russian Academic Excellence Project “5-100.”
This paper is a detailed and extended version of the talk presented at the CMStatistics (ERCIM) 2015 Conference. The author’s attendance on the conference was partially supported by the COST Action IC1408—CRoNoS.
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Batagelj, V. (2020). Corrected Overlap Weight and Clustering Coefficient. In: Ragozini, G., Vitale, M. (eds) Challenges in Social Network Research. Lecture Notes in Social Networks. Springer, Cham. https://doi.org/10.1007/978-3-030-31463-7_1
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DOI: https://doi.org/10.1007/978-3-030-31463-7_1
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