We survey the concept of assortativity, starting from its original definition by Newman in 2002. Degree assortativity is the most commonly used form of assortativity. Degree assortativity is extensively used in network science. Since degree assortativity alone is not sufficient as a graph analysis tool, assortativity is usually combined with other graph metrics. Much of the research on assortativity considers undirected, non-weighted networks. The research on assortativity needs to be extended to encompass also directed links and weighted links. In addition, the relation between assortativity and line graphs, complementary graphs and graph spectra needs further work, to incorporate directed graphs and weighted links. The present survey paper aims to summarize the work in this area and provides a new scope of research.

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