On the Randi\'{c} index and its variants of network data
Mingao Yuan

TL;DR
This paper derives theoretical limits for the Randić index and its variants in inhomogeneous Erdős-Rényi random graphs, revealing how network heterogeneity influences these network statistics and applying findings to real-world networks.
Contribution
It provides the first theoretical derivation of bounds for the Randić index in inhomogeneous Erdős-Rényi graphs, enhancing understanding of network heterogeneity effects.
Findings
Derived limits of Randić index for inhomogeneous Erdős-Rényi graphs
Showed how heterogeneity impacts the Randić index
Applied indices to real-world network data
Abstract
Summary statistics play an important role in network data analysis. They can provide us with meaningful insight into the structure of a network. The Randi\'{c} 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 Randi\'{c} 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 Erd\H{o}s-R\'{e}nyi random graph by simulation. In this paper, we shall derive the limits of the Randi\'{c} index and its variants of an inhomogeneous Erd\H{o}s-R\'{e}nyi random graph. Our results charaterize how network heterogeneity affects the indices and provide new insights about the Randi\'{c} index and its…
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Taxonomy
TopicsComplex Network Analysis Techniques · Graph theory and applications · Advanced Clustering Algorithms Research
