  Many time-evolving systems in nature, society and technology leave traces of
the interactions within them. These interactions form temporal networks that
reflect the states of the systems. In this work, we pursue a coarse-grained
description of these systems by proposing a method to assign discrete states to
the systems and inferring the sequence of such states from the data. Such
states could, for example, correspond to a mental state (as inferred from
neuroimaging data) or the operational state of an organization (as inferred by
interpersonal communication). Our method combines a graph distance measure and
hierarchical clustering. Using several empirical data sets of social temporal
networks, we show that our method is capable of inferring the system's states
such as distinct activities in a school and a weekday state as opposed to a
weekend state. We expect the methods to be equally useful in other settings
such as temporally varying protein interactions, ecological interspecific
interactions, functional connectivity in the brain and adaptive social
networks.
