assortativ

Assortativ is a term used in discussions of network structure to describe a tendency for nodes to connect with others that are similar with respect to certain attributes. In English-language literature the closely related concepts are assortativity and assortative mixing, but assortativ appears in some languages as an equivalent adjective.

Definition and meaning

In network science, assortativity measures how strongly a network tends to link nodes with similar characteristics. The core statistic is the assortativity coefficient, often denoted r. For numerical node attributes, r is the Pearson correlation coefficient of the attribute values at the two ends of each edge. For categorical attributes, r can be defined in terms of the joint distribution of category labels at either end of edges. Values range from −1 to +1, where positive values indicate homophily or preference for similar nodes, negative values indicate a tendency to connect with dissimilar nodes, and around zero suggests no particular pattern.

Types and examples

Degree assortativity concerns whether high-degree nodes connect to other high-degree nodes. Attribute or category assortativity concerns other properties such as age, education, or biological traits. Social networks often exhibit positive assortativity by age or status, while some technological or biological networks may show disassortativity by degree.

Applications and interpretation

Assortativ patterns influence network processes, including information diffusion, robustness, and epidemic spread. Positive assortativity can slow some diffusion processes but strengthen community structure, whereas disassortativity can promote rapid spreading across diverse parts of a network.

See also

Network theory, assortative mating, homophily, disassortativity. Note that for some languages, assortativ serves as a direct translation of the concept of assortativity or assortative mixing.