  Motifs are the fundamental components of complex systems. The topological
structure of networks representing complex systems and the frequency and
distribution of motifs in these networks are intertwined. The complexities
associated with graph and subgraph isomorphism problems, as the core of
frequent subgraph mining, have direct impacts on the performance of motif
discovery algorithms. To cope with these complexities, researchers have adopted
different strategies for candidate generation and enumeration, and frequency
computation. In the past few years, there has been an increasing interest in
the analysis and mining of temporal networks. These networks, in contrast to
their static counterparts, change over time in the form of insertion, deletion,
or substitution of edges or vertices or their attributes. In this paper, we
provide a survey of motif discovery algorithms proposed in the literature for
mining static and temporal networks and review the corresponding algorithms
based on their adopted strategies for candidate generation and frequency
computation. As we witness the generation of a large amount of network data in
social media platforms, bioinformatics applications, and communication and
transportation networks and the advance in distributed computing and big data
technology, we also conduct a survey on the algorithms proposed to resolve the
CPU-bound and I/O bound problems in mining static and temporal networks.
