Abstract
<p><span style="font-size: 10.5pt; font-family: 'Times New Roman','serif'; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">Assortativity index (<em>A. Index</em>) of real-world network graphs has been traditionally computed based on the degree centrality metric and the networks were classified as assortative, dissortative or neutral if the <em>A. Index</em> values are respectively greater than 0, less than 0 or closer to 0. In this paper, we evaluate the <em>A. Index</em> of real-world network graphs based on some of the commonly used centrality metrics (betweenness, eigenvector and closeness) in addition to degree centrality and observe that the assortativity classification of real-world network graphs depends on the node-level centrality metric used. We also propose five different levels of assortativity (strongly assortative, weakly assortative, neutral, weakly dissortative and strongly dissortative) for real-world networks and the corresponding range of <em>A. Index</em> value for the classification. We analyze a collection of 50 real-world network graphs with respect to each of the above four centrality metrics and estimate the empirical probability of observing a real-world network graph to exhibit a particular level of assortativity. We claim that a real-world network graph is more likely to be neutral with respect to the betweenness and degree centrality metrics and more likely to be assortative with respect to the eigenvector and closeness centrality metrics.</span></p>
Highlights
An interesting and significant observation from the color-coded Table 3 is that for real-world networks with two or three levels of assortativity with the centrality metrics: the level of assortativity typically exhibited a transition from dissortative to neutral neutral to weakly assortative to strongly assortative when the centrality metrics are considered in this order: betweenness centrality (BWC), degree centrality (DegC), eigenvector centrality (EVC) and closeness centrality (ClC)
We have shown that the assortativity classification of real-world network graphs is dependent on the node-level centrality metric used to compute the assortativity index values of the edges
We observe about 80% of the real-world network graphs to exhibit more than one assortativity level: 56% exhibiting two assortativity levels and 24% exhibiting three assortativity levels
Summary
For 40 of the 50 real-world networks analyzed, we observe that the level of classification of the network (strongly or weakly assortative, neutral, strongly or weakly dissortative) depends on the centrality metric under consideration. Since we have analyzed a vast collection of networks with varying levels of complexity, we use the results of our assortativity analysis to empirically propose the likelihood of a real-world network being classified neutral or assortative (strongly assortative or weakly assortative) with respect to a particular centrality metric. To the best of our knowledge, we have not come across a paper that has conducted a comprehensive assortativity analysis of complex real-world networks with respect to the four commonly used centrality metrics as well as empirically proposed the likelihood of observing a real-world network to be neutral, strongly assortative or weakly assortative with respect to a particular centrality metric. All the real-world networks analyzed in this paper are modeled as undirected graphs
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
