Revealing evolutions in dynamical networks

The description of large temporal graphs requires effective methods giving an appropriate mesoscopic partition. Many approaches exist today to detect “communities”, ie groups of nodes that are densely connected (Fortunato, 2010), in static graphs. However, many networks are intrinsically dynamical, and need a dynamic mesoscale description, as interpreting them as static networks would cause loss of important information (Holme and Saramaki, 2012; Holme 2015). For example, dynamic processes such as the emergence of new scientific disciplines, their fusion, split or death need a mesoscopic description of the evolving network of scientific articles. There are two straightforward approaches to describe an evolving network using methods developed for static networks. The first finds the community structure of the ​aggregated network, ie the network found by aggregating the nodes and their links at all times. However, this approach discards most temporal information, and may lead to inappropriate descriptions, as very different dynamic data can give rise to the identical static graphs (Berger-Wolf and Saia, 2006). To avoid this problem, the opposite approach closely follows the evolutions and builds networks for successive time slices by selecting the relevant nodes and edges. Then, the mesoscopic structure of each of these slices is found ​independently and the structures are connected in various ways to obtain a temporal description (Berger-Wolf and Saia, 2006; G. Palla et al, 2007, Rosvall and Bergstrom, 2010, Chavalarias and Cointet, 2013). By using an optimal structural description at each time slice, this method avoids the inertia of the aggregated approach. Its main drawback lies in the inherent fuzziness of the communities, which leads to “noise” and artificial mesoscopic evolutions, with no counterpart in the real evolutions of the data. For example, rather different partitions have a very close modularity (Good et al, 2010), and minor changes in the network may lead to quite different partitions in successive time slices, which would be inadequately interpreted as major structural changes. Several methods have been proposed to overcome the problems of these two extreme approaches (Gauvin et al. 2015, Peel and Clauset, 2014, Mucha et al, 2010, Kawadia and Sreenivasan 2012). Here, we present a new approach that distinguishes real trends and noise in the mesoscopic description of social data using the continuity of social evolutions. To be able to