Exploring Temporal Networks with Greedy Walks

TL;DR

This paper investigates the structure of temporal networks using greedy walks, revealing that correlated contact patterns like burst trains significantly influence walk behavior and predictability.

Contribution

It introduces the use of greedy walks as probes to uncover temporal-topological patterns and demonstrates their sensitivity to correlated contact sequences in temporal networks.

Findings

Greedy walks often get trapped in small node sets due to contact correlations.

Burst trains are identified as a dominant factor affecting walk coverage.

Sequences of visited nodes are more predictable in real data than in reference models.

Abstract

Temporal networks come with a wide variety of heterogeneities, from burstiness of event sequences to correlations between timings of node and link activations. In this paper, we set to explore the latter by using greedy walks as probes of temporal network structure. Given a temporal network (a sequence of contacts), greedy walks proceed from node to node by always following the first available contact. Because of this, their structure is particularly sensitive to temporal-topological patterns involving repeated contacts between sets of nodes. This becomes evident in their small coverage per step as compared to a temporal reference model -- in empirical temporal networks, greedy walks often get stuck within small sets of nodes because of correlated contact patterns. While this may also happen in static networks that have pronounced community structure, the use of the temporal reference model takes the underlying static network structure out of the equation and indicates that there is a purely temporal reason for the observations. Further analysis of the structure of greedy walks indicates that burst trains, sequences of repeated contacts between node pairs, are the dominant factor. However, there are larger patterns too, as shown with non-backtracking greedy walks. We proceed further to study the entropy rates of greedy walks, and show that the sequences of visited nodes are more structured and predictable in original data as compared to temporally uncorrelated references. Taken together, these results indicate a richness of correlated temporal-topological patterns in temporal networks.