  Networks are used as highly expressive tools in different disciplines. In
recent years, the analysis and mining of temporal networks have attracted
substantial attention. Frequent pattern mining is considered an essential task
in the network science literature. In addition to the numerous applications,
the investigation of frequent pattern mining in networks directly impacts other
analytical approaches, such as clustering, quasi-clique and clique mining, and
link prediction. In nearly all the algorithms proposed for frequent pattern
mining in temporal networks, the networks are represented as sequences of
static networks. Then, the inter- or intra-network patterns are mined. This
type of representation imposes a computation-expressiveness trade-off to the
mining problem. In this paper, we propose a novel representation that can
preserve the temporal aspects of the network losslessly. Then, we introduce the
concept of constrained interval graphs (CIGs). Next, we develop a series of
algorithms for mining the complete set of frequent temporal patterns in a
temporal network data set. We also consider four different definitions of
isomorphism to allow noise tolerance in temporal data collection. Implementing
the algorithm for three real-world data sets proves the practicality of the
proposed algorithm and its capability to discover unknown patterns in various
settings.
