Analytical and statistical studies of Rodriguez-Velazquez indices Articles uri icon

publication date

  • May 2021

start page

  • 1246

end page

  • 1259

issue

  • 5

volume

  • 59

International Standard Serial Number (ISSN)

  • 0259-9791

Electronic International Standard Serial Number (EISSN)

  • 1572-8897

abstract

  • In this work we perform analytical and statistical studies of the Rodríguez–
    Velázquez (RV) indices on graphs G. The topological RV(G) indices, recently
    introduced in Rodríguez–Velázquez and Balaban (J Math Chem 57:1053, 2019),
    are based on graph adjacency matrix eigenvalues and eigenvectors. First, we analytically
    obtain new relations connecting RV(G) with the graph energy E(G) and the
    subgraph centrality EE(G), the later being proportional to the well known Estrada
    index. Then, within a random matrix theory (RMT) approach we statistically validate
    our relations on ensembles of randomly-weighted Erdős–Rényi graphs G(n, p),
    characterized by n vertices connected independently with probability p ∈ (0, 1) .
    Additionally, we show that the ratio ⟨RV(G(n, p))⟩∕⟨RV(G(n, 0))⟩ scales with the
    average degree ⟨k⟩ = (n − 1)p.

subjects

  • Statistics

keywords

  • rodriguez–velazquez indices; eigenvalue-based topological index; erdős–rényi graphs