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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.