Hitting times and resistance distances of q-triangulation graphs: Accurate results and applications

07/29/2018
by   Yibo Zeng, et al.
0

Graph operations or products, such as triangulation and Kronecker product have been extensively applied to model complex networks with striking properties observed in real-world complex systems. In this paper, we study hitting times and resistance distances of q-triangulation graphs. For a simple connected graph G, its q-triangulation graph R_q(G) is obtained from G by performing the q-triangulation operation on G. That is, for every edge uv in G, we add q disjoint paths of length 2, each having u and v as its ends. We first derive the eigenvalues and eigenvectors of normalized adjacency matrix of R_q(G), expressing them in terms of those associated with G. Based on these results, we further obtain some interesting quantities about random walks and resistance distances for R_q(G), including two-node hitting time, Kemeny's constant, two-node resistance distance, Kirchhoff index, additive degree-Kirchhoff index, and multiplicative degree-Kirchhoff index. Finally, we provide exact formulas for the aforementioned quantities of iterated q-triangulation graphs, using which we provide closed-form expressions for those quantities corresponding to a class of scale-free small-world graphs, which has been applied to mimic complex networks.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/14/2023

On the degree-Kirchhoff index, Gutman index and the Schultz index of pentagonal cylinder/ Möbius chain

The degree-Kirchhoff index of a graph is given by the sum of inverses of...
research
02/27/2020

Edge corona product as an approach to modeling complex simplical networks

Many graph products have been applied to generate complex networks with ...
research
05/30/2022

Edge coloring of graphs of signed class 1 and 2

Recently, Behr introduced a notion of the chromatic index of signed grap...
research
09/14/2017

Extended corona product as an exactly tractable model for weighted heterogeneous networks

Various graph products and operations have been widely used to construct...
research
02/08/2023

Resistance Distances in Directed Graphs: Definitions, Properties, and Applications

Resistance distance has been studied extensively in the past years, with...
research
08/29/2021

The Popularity-Homophily Index: A new way to measure Homophily in Directed Graphs

In networks, the well-documented tendency for people with similar charac...
research
01/09/2023

Combinatorial Properties for a Class of Simplicial Complexes Extended from Pseudo-fractal Scale-free Web

Simplicial complexes are a popular tool used to model higher-order inter...

Please sign up or login with your details

Forgot password? Click here to reset