AN ANALYSIS OF THE FAT-TAILEDNESS OF THE CENTRALITY DISTRIBUTIONS OF REAL-WORLD NETWORKS

Natarajan Meghanathan Jackson State University, MS, USA 

ABSTRACT 

"Kurtosis" has long been considered an appropriate measure to quantify the extent of fat-tailedness of the degree distribution of a complex real-world network. However, the Kurtosis values for more than one realworld network have not been studied in conjunction with other statistical measures that also capture the extent of variation in node degree. Also, the Kurtosis values of the distributions of other commonly centrality metrics for real-world networks have not been analyzed. In this paper, we determine the Kurtosis values for a suite of 48 real-world networks along with measures such as SPR(K), Max(K)-Min(K), Max(K)-Avg(K), SD(K)/Avg(K), wherein SPR(K), Max(K), Min(K), Avg(K) and SD(K) represent the spectral radius ratio for node degree, maximum node degree, minimum node degree, average and standard deviation of node degree respectively. Contrary to the conceived notion in the literature, we observe that real-world networks whose degree distribution is Poisson in nature (characterized by lower values of SPR(K), Max(K)-Min(K), Max(K)-Avg(K), SD(K)/Avg(K)) could have Kurtosis values that are larger than that of real-world networks whose degree distribution is scale-free in nature (characterized by larger values of SPR(K), Max(K)-Min(K), Max(K)-Avg(K), SD(K)/Avg(K)). We also observe the Kurtosis values of the betweenness centrality distributions of the real-world networks to be more likely the largest among the Kurtosis values with respect to the commonly studied centrality metrics. 

KEYWORDS

 Fat-tailedness, Degree Distribution, Kurtosis, Real-World Networks, Centrality Metrics, Concordance  

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