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 ( $CIG$ s). 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 for accommodating minor variations in temporal data of networks. Implementing the algorithm for three real-world data sets proves the practicality of the proposed approach and its capability to discover unknown patterns in various settings.

Networks are known as perfect tools for modeling various types of systems. In the literature of network mining, frequent subgraph mining is considered as the essence of mining network data. In this problem, the dataset is composed of networks representing multiple independent systems or one system at multiple time stamps. The cores of mining frequent subgraphs are graph and subgraph isomorphism. Due to the complexities of these problems, the frequent subgraph mining algorithms proposed in the literature employ various heuristics for candidate generation, duplicate subgraphs pruning, and support computation. In this survey, we provide a classification of proposed algorithms in the literature. The algorithms for static networks have found numerous applications. Therefore, these algorithms will be reviewed in detail. Besides, it is discussed that consideration of temporality of data can impact the derived insight and attracted substantial attention in recent years. However, prior surveys have not comprehensively examined the algorithms of frequent subgraph mining in a database of temporal networks represented as network snapshots. Therefore, the algorithms proposed for mining frequent subgraphs in temporal networks are reviewed. Moreover, most of the surveys have focused on main-memory algorithms. Here, we review disk-based, parallel, and distributed algorithms proposed for mining frequent subgraphs.