Past Networks Seminar

Temporal networks are increasingly being used to model the interactions of complex systems. 
Most studies require the temporal aggregation of edges (or events) into discrete time steps to perform analysis.
In this article we describe a static, behavioural representation of a temporal network, the temporal event graph (TEG).
The TEG describes the temporal network in terms of both inter-event time and two-event temporal motifs.
By considering the distributions of these quantities in unison we provide a new method to characterise the behaviour of individuals and collectives in temporal networks as well as providing a natural decomposition of the network.
We illustrate the utility of the TEG by providing examples on both synthetic and real temporal networks.

Identifying clusters or "communities" of densely connected nodes in networks is an active area of research, with relevance to many applications. Recent advances in the field have focused especially on temporal, multiplex, and other kinds of multilayer networks.

One method for detecting communities in multilayer networks is to maximise a generalised version of an objective function known as modularity. Writing down multilayer modularity requires the specification of two types of resolution parameters, and choosing appropriate values is crucial for uncovering meaningful community structure. In the simplest case, there are just two parameters, one controlling the sizes of detected communities, and the other influencing how much communities change from layer to layer. By establishing an equivalence between modularity optimisation and a multilayer maximum-likelihood approach to community detection, we are able to determine statistically optimal values for these two parameters. 

When applied to existing multilayer benchmarks, our optimized approach performs significantly better than using parameter choices guided by heuristics. We also apply the method to supermarket data, revealing changes in consumer behaviour over time.