Exploring temporal networks with greedy walks*
1 Department of Computer Science, Aalto
University School of Science, P.O.
Box 15400, 00076
2 Department of Energy Science, Sungkyunkwan University, 440-746 Suwon, Korea
Received in final form: 19 October 2015
Published online: 14 December 2015
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 temporal greedy walks as probes of temporal network structure. Given a temporal network (a sequence of contacts), temporal 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 taken 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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2015