Multiplicative topological indices: Analytical properties and application to random networks

2023/06/05 by R. Aguilar-Sanchez, J. A. Méndez‐Bermúdez, Aguilar-Sanchez, R. +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2306.02511

openalex publication_date 2023/06/05 · openalex created_date 2023/06/07 · openalex updated_date 2026/08/01

Abstract

We make use of multiplicative degree-based topological indices X_Π(G) to perform a detailed analytical and statistical study of random networks G=(V(G),E(G)). We consider two classes of indices: X_Π(G) = ∏_{u ∈ V(G)} F_V(d_u) and X_Π(G) = ∏_{uv ∈ E(G)} F_E(d_u,d_v), where uv denotes the edge of G connecting the vertices u and v, d_u is the degree of the vertex u, and F_V(x) and F_E(x,y) are functions of the vertex degrees. Specifically, we find analytical inequalities involving these multiplicative indices. Also, we apply X_Π(G) on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. We show that < ln X_Π(G) >, normalized to the order of the network, scale with the corresponding average degree; here < ⋅ > denotes the average over an ensemble of random networks.

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