Dependence of the average to-node distance on the node degree for random graphs and growing networks

TL;DR

This paper investigates how the average distance to nodes depends on their degree in various types of networks, including random, scale-free, and exponential growing networks, with implications for search strategies.

Contribution

It introduces an algorithm for constructing the distance matrix and applies it to analyze the dependence of node distance on degree in different network models.

Findings

Distance to nodes varies with node degree in different network types

Results inform search strategies in complex networks

Analysis covers random, scale-free, and exponential networks

Abstract

In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\xi$ to other nodes). Here we investigate how $\xi$ depends on $k$. Our earlier algorithm of the construction of the distance matrix is applied to the random graphs. Numerical calculations are performed for the random graphs and the growing networks: the scale-free ones and the exponential ones. The results are relevant for search strategies in different networks.