The structured backbone of temporal social ties

Abstract

In many data sets, crucial 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, the "network backbone", is a non-trivial task, and methods put forward until now do not address time-resolved networks, whose availability has strongly increased in recent years. We develop here such a method, by defining an adequate temporal network null model, which calculates the random chance of nodes to be connected at any time after controlling for their activity. This allows us to identify, at any level of statistical significance, pairs of nodes that have more interactions than expected given their activities: These form a backbone of significant ties. We apply our method to empirical temporal networks of socio-economic interest and find that (i) at given level of statistical significance, our method identifies more significant ties than methods considering temporally aggregated networks, and (ii) when a community structure is present, most significant ties are intra-community edges, suggesting that the weights of inter-community edges can be explained by the null model of random interactions. Most importantly, our filtering method can assign a significance to more complex structures such as triads of simultaneous interactions, while methods based on static representations are by construction unable to do so. Strikingly, we uncover that significant triads are not equivalent to triangles composed by three significant edges. Our results hint at new ways to represent temporal networks for use in data-driven models and in anonymity-preserving ways.

Weight thresholding on complex networks

“…Analyzing very dense graphs with tools of network science is often impossible, unless some pre-processing technique is applied to reduce the number of connections. Different recipes of edge pruning, or graph sparsification, have been proposed in recent years [4][5][6][7][8][9][10].…”

A primer on statistically validated networks

“…The names proposed so far are (i) backbone of a network [10], and (ii) statistically validated network [11]. Selection of nodes or links not consistent with a null hypothesis have been investigated in studies focusing on classic examples of networks [10,11], trading decisions of investors [12,13,14,15], criminal career of a large set of suspects [16], mobile phone calls of large set of users [17,18], financial credit transactions occurring in an Interbank market [19], intraday lead-lag relationships of returns of financial assets traded in major financial markets [20], the Japanese credit market [22], the socio-technical system of air traffic management [23], the core of communities observed in projected networks originating from bipartite networks [24], the international trade [25], and temporal social ties observed in face to face interactions [26].…”