Abstract
In many data sets, information on the structure and temporality of a system coexists with noise and non-essential elements. In networked systems for instance, some edges might be non-essential or exist only by chance. Filtering them out and extracting a set of relevant connections is a non-trivial task. Moreover, mehods put forward until now do not deal with time-resolved network data, which have become increasingly available. Here we develop a method for filtering temporal network data, by defining an adequate temporal null model that allows us to identify pairs of nodes having more interactions than expected given their activities: the significant ties. Moreover, our method can assign a significance to complex structures such as triads of simultaneous interactions, an impossible task for methods based on static representations. Our results hint at ways to represent temporal networks for use in data-driven models.
Highlights
In many data sets, information on the structure and temporality of a system coexists with noise and non-essential elements
A highly active node could in principle have a large number of ties, so that one needs to control for the difference in intrinsic activity levels across nodes to extract statistically significant ties that cannot be explained by random chance
This null model can be interpreted as a configuration or fitness model, whose parameters are estimated by using global information, to the enhanced configuration model (ECM) filter for static networks[17]
Summary
Information on the structure and temporality of a system coexists with noise and non-essential elements. We develop a method to extract an irreducible backbone from a sequence of temporal contacts between nodes, by defining an adequate temporal null model This null model can be interpreted as a (temporal) configuration or fitness model, whose parameters are estimated by using global information (the numbers of contacts for all node pairs), to the enhanced configuration model (ECM) filter for static networks[17]. Thanks to this null model, we determine the set of significant ties, at any significance level, among all the pairs of nodes having interacted. By construction, such a task would be impossible when defining significant ties and backbones directly from a temporally aggregated network
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