# Random walks on activity-driven networks with attractiveness

## TL;DR

This paper introduces a dynamic network model incorporating node activity and attractiveness, analyzing their impact on random walk processes with analytical solutions and empirical relevance.

## Contribution

It presents a novel time-varying network model with analytical insights into how activity and attractiveness influence random walks.

## Key findings

- Heterogeneous activity and attractiveness significantly affect random walk dynamics.
- Analytical solutions for stationary state and mean first passage time are derived.
- Empirical social network data inform the model and results.

## Abstract

Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously distributed. Here, we present a time-varying network model where each node and the dynamical formation of ties are characterised by these two features. We study how these properties affect random walk processes unfolding on the network when the time scales describing the process and the network evolution are comparable. We derive analytical solutions for the stationary state and the mean first passage time of the process and we study cases informed by empirical observations of social networks. Our work shows that previously disregarded properties of real social systems such heterogeneous distributions of activity and attractiveness as well as the correlations between them, substantially affect the dynamical process unfolding on the network.