Motif discovery in networks: A survey

Motifs are regarded as network blocks because motifs can be used to present fundamental patterns in networks. Motif discovery is well applied in various scientific problems, including subgraph mining and graph isomorphism tasks. This paper analyzes and summarizes current motif discovery algorithms in the field of network science with both efficiency and accuracy perspectives. In this paper, we present motif discovery algorithms, including MFinder, FanMod, Grochow, MODA, Kavosh, G-tries, QuateXelero, color-coding approaches, and GPU-based approaches. Based on that, we discuss the real-world applications of the algorithms mentioned above under different scenarios. Since motif discovery algorithms are diffusely demanded in many applications, several challenges may be firstly handled, including high computational complexity, higher order motif discovery, same motif detection, discovering heterogeneous sizes of motifs, as well as motif discovery results visualization. This work sheds light on current research progress and future research orientations.