Temporal Betweenness Centrality

Ordinary betweenness counts shortest paths in a static graph where all edges are simultaneously available. Temporal betweenness only counts paths that can be traversed in chronological order, so a node must be active at the right times to score highly — not just be structurally well-connected.

Three common criteria are earliest-arrival time (minimize when the path ends), fastest path (minimize elapsed duration), and minimum hop count. For epidemiology or information spread, earliest-arrival is most natural. For efficiency analysis, fastest path is often preferred. Report your choice explicitly.

Exact TBC computation is computationally costly for large networks. Approximation algorithms exist that sample source nodes and scale better. Libraries such as Teneto (Python) and snapshot-based approaches in NetworkX can help, but always benchmark runtime before attempting full computation on millions of events.

Simultaneous edges break strict time-ordering. Decide in advance whether simultaneous contacts are treated as ordered (randomly or by another criterion) or as unordered within a time step. Document your assumption, as it can meaningfully change which paths are valid.

Such a node is not a structural hub but is temporally well-placed: it is active at moments that link otherwise separate temporal trajectories. It is a time-sensitive broker, whose influence depends on when it is active, not just whom it knows.