### On the Sufficiency of Using Degree Sequence of the Vertices to Generate Random Networks Corresponding to Real-World Networks

#### Abstract

The focus of research in this paper is to investigate whether a random network whose degree sequence of the vertices is the same as the degree sequence of the vertices in a real-world network would exhibit values for other analysis metrics similar to those of the real-world network. We use the well-known Configuration Model to generate a random network on the basis of the degree sequence of the vertices in a real-world network wherein the degree sequence need not be Poisson-style. The extent of similarity between the vertices of the random network and real-world network with respect to a particular metric is evaluated in the form of the correlation coefficient of the values of the vertices for the metric. We involve a total of 24 real-world networks in this study, with the spectral radius ratio for node degree (measure of variation in node degree) ranging from 1.04 to 3.0 (i.e., from random networks to scale-free networks). We consider a suite of seven node-level metrics and three network-level metrics for our analysis and identify the metrics for which the degree sequence would be just sufficient to generate random networks that have a very strong correlation (correlation coefficient of 0.8 or above) with that of the vertices in the corresponding real-world networks.

#### Keywords

Configuration model; degree sequence; correlation; random network; real-world network

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