Events in complex systems — turbulent droplet arrivals, heartbeats, earthquakes, neural spikes — occur at irregular intervals. The gaps between events carry information about the underlying dynamics. Existing statistical measures can tell you whether events tend to cluster (shorter gaps than expected) or repel (longer gaps), but they compress this into a single number: an overall clustering tendency. The internal structure of individual clusters — which events belong together, how clusters differ from each other, where one cluster ends and another begins — is lost.
The network approach converts the irregular time series into a graph. Each event is a node. Edges connect events that are close in time, with weights reflecting temporal proximity. Community detection algorithms then partition the graph into clusters — groups of events that are more closely associated with each other than with events in other groups. The method identifies not just that clustering exists but which events form which clusters, how large each cluster is, and how they are distributed in time.
Validation on Poisson processes (no clustering by construction) confirms the method does not hallucinate structure. Application to turbulent droplet arrivals reveals cluster sizes and inter-cluster intervals that existing statistics could not resolve. Application to ECG data identifies heartbeat groupings with clinically interpretable structure.
The through-claim is about representation choice. A time series of event arrival times is one-dimensional — a list of numbers. By mapping it to a network, the data gains a second dimension: connectivity. The community structure that emerges in the network is not visible in the time series itself, not because it isn't there but because the time series representation doesn't have the vocabulary to express it. The network doesn't add information; it adds structure to the information that was already present.
(arXiv:2603.18044)