Fifty years of graph matching, network alignment and network comparison

In this paper we survey methods for performing a comparative graph analysis and explain the history, foundations and differences of such techniques of the last 50 years. While surveying these methods, we introduce a novel classification scheme by distinguishing between methods for deterministic and random graphs. We believe that this scheme is useful for a better understanding of the methods, their challenges and, finally, for applying the methods efficiently in an interdisciplinary setting of data science to solve a particular problem involving comparative network analysis.