On the Randic index and its variants of network data

The Summary statistics play an important role in network data analysis. They can provide us with meaningful insight into the structure of a network. The Randic index is one of the most popular network statistics that has been widely used for quantifying information of biological networks, chemical networks, pharmacologic networks, etc. A topic of current interest is to find bounds or limits of the Randic index and its variants. A number of bounds of the indices are available in literature. Recently, there are several attempts to study the limits of the indices in the Erdos-Renyi random graph by simulation. In this paper, we shall derive the limits of the Randic index and its variants of an inhomogeneous Erdos-Renyi random graph. Our results charaterize how network heterogeneity affects the indices and provide new insights about the Randic index and its variants. Finally we apply the indices to several real-world networks.