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The Sombor indices, a new category of degree-based topological moleculardescriptors, have been widely investigated due to their excellent chemicalapplicability. This paper aims to establish Sombor indices distributions inrandom polygonal chain networks and to achieve expressions of the expectedvalues and variances. The expected values and variances of the Sombor indicesfor polyonino, pentachain, polyphenyl, and cyclooctane chains are obtained.Since the end connection of a random chain network follows a binomialdistribution, the Sombor indices of any chain network follow the normaldistribution when the number of polygons connected by the chain, indicated byn, approaches infinity. Keywords: Degree distribution; Polygonal chains;Expected value; Variance; Sombor indices.

The statistical analysis for Sombor indices in a random polygonal chain networks