Algorithms for graph and network analysis: Graph alignment

In this article we discuss the problem of graph alignment, which has been longly referred to for the purpose of analyzing and comparing biological networks. In particular, we describe different facets of graph alignment, according to the number of input networks, the fixed output objective, the possible heterogeneity of input data. Accordingly, we will discuss pairwise and multiple alignment, global and local alignment, etc. Moreover, we provide a comprehensive overview of the algorithms and techniques proposed in the literature to solve each of the specific considered types of graph alignment. In order to make the material presented here complete and useful to guide the reader in the use of the alignment algorithms, we also illustrate available software tools implementing some of the techniques proposed in the literature. Finally, we discuss the main emerging research directions on this topic.