**Author**: Natarajan Meghanathan

**Affiliation**: Jackson State University, MS

**Country**: USA

**Category**: Computer Science & Information Technology

**Volume, Issue, Month, Year**: 7, 8, June,

**Abstract**

"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.

**Keyword**: Fat-tailedness, Degree Distribution, Kurtosis, Real-World Networks, Kendall's Concordancebased Correlation Coefficient

**For More Details**: https://airccj.org/CSCP/vol7/csit77007.pdf

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