Many networks are treated as static objects, although they are in fact strongly time-dependent. This can have a dramatic impact on the possible spreading patterns for infectious diseases.
A static (aggregated) trade network is constructed as follows: if two nodes are connected directly to each other in a time-dependent network, the same connection is present in the static network. A fundamental difference between the static and the time dependent view however, is the consideration of paths, i.e. indirect connections over more than one edge. Concerning paths, the causality of the edges used plays an essential role. In an aggregated network, paths can seem causal, although they do not follow a time-respecting sequence of edges in the real system. This leads to a systematic overestimation of outbreak sizes, if time-dependent networks are treated as static.
We introduce a new method, which allows for the computation of the total causal path structure of a temporal network (represented by its accessibility graph) using the adjacency matrices of its snapshots. In addition, information about the timescales required for path traversal can be derived from the step-by-step derivation of the accessibility graph of the network. This procedure directly yields the distribution of shortest path durations in a temporal network. In addition, we define the new measure causal fidelity that compares the number of paths in a temporal network with its aggregated counterpart. This measure allows a quantitative assessment of how well a temporal network can be approximated by a static aggregated one.
The methods presented here require only basic knowledge linear algebra and can be implemented efficiently. Their capability is demonstrated for three examples: networks of social contacts, livestock trade, and sexual contacts.
Einladender: Prof. Thomas Ihle
Ort: Großer Seminarraum
Zeit: 14:00 Uhr