# Concurrency and reachability in tree-like temporal networks

## TL;DR

This paper investigates how temporal properties like concurrency and structural cohesion influence reachability in tree-like temporal networks, affecting spreading processes such as contagions.

## Contribution

It introduces a new framework for analyzing reachability based on temporal concurrency and cohesion, with models and simulations for random networks.

## Key findings

- Higher temporal concurrency increases reachability.
- Structural cohesion correlates with greater reachability.
- Models accurately predict reachability in various network configurations.

## Abstract

Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes and links appear and disappear. We focus on the effects of "accessibility", whether there is a temporally consistent path from one node to another, and "reachability", the density of the corresponding "accessibility graph" representation of the temporal network. The level of reachability thus inherently limits the possible extent of any spreading process on the temporal network. We study reachability in terms of the overall levels of temporal concurrency between edges and the structural cohesion of the network agglomerating over all edges. We use simulation results and develop heterogeneous mean field model predictions for random networks to better quantify how the properties of the underlying temporal network regulate reachability.