"Kurtosis" has long been considered an appropriate measure to quantify the extent of fattailedness
of the degree distribution of a complex real-world network. However, the Kurtosis
values for more than one real-world network have not been studied in conjunction with other
statistical measures that also capture the extent of variation in node degree. 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 realworld
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)). When evaluated for any two realworld
networks among all the 48 real-world networks, the Kendall's concordance-based
correlation coefficients between Kurtosis and each of SPR, Max(K)-Min(K), Max(K)-Avg(K)
and SD(K)/Avg(K) are 0.40, 0.26, 0.34 and 0.50 respectively. Thus, we seriously question the
appropriateness of using Kurtosis to compare the extent of fat-tailedness of the degree
distribution of the vertices for any two real-world networks.

User Name : alex

Posted 26-04-2018 on 22:21:45 AEDT

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