Authors:
Mingao Yuan
Abstract
The Randić index is a popular topological graph index that measures the extent of branching of a graph. It has many
applications in chemistry and network data analysis. In this paper, we study the limiting distribution of the Randić
index in a random geometric graph. We prove that the centered and scaled Randić index converges in law to an
infinite sum of functions of independent chi-square random variables. It is interesting that the limiting distribution
is not the standard normal distribution as in the Erdős-Rényi random graph case. However, the Randić index
of the random geometric graph is asymptotically the same as the Erdős-Rényi random graph.
