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We propose a method to search for signs of causal structure in spatiotemporaldata making minimal a priori assumptions about the underlying dynamics. To thisend, we generalize the elementary concept of recurrence for a point process intime to recurrent events in space and time. An event is defined to be arecurrence of any previous event if it is closer to it in space than all theintervening events. As such, each sequence of recurrences for a given event isa record breaking process. This definition provides a strictly data driventechnique to search for structure. Defining events to be nodes, and linkingeach event to its recurrences, generates a network of recurrent events.Significant deviations in properties of that network compared to networksarising from random processes allows one to infer attributes of the causaldynamics that generate observable correlations in the patterns. We deriveanalytically a number of properties for the network of recurrent eventscomposed by a random process. We extend the theory of records to treat not onlythe variable where records happen, but also time as continuous. In this way, weconstruct a fully symmetric theory of records leading to a number of newresults. Those analytic results are compared to the properties of a networksynthesized from earthquakes in Southern California. Significant disparitiesfrom the ensemble of acausal networks that can be plausibly attributed to thecausal structure of seismicity are: (1) Invariance of network statistics withthe time span of the events considered, (2) Appearance of a fundamental lengthscale for recurrences, independent of the time span of the catalog, which isconsistent with observations of the ``rupture length'', (3) Hierarchy in thedistances and times of subsequent recurrences.Comment: 19 pages, 13 figure

Networks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity