disassortativity

Disassortativity is a property of networks in which nodes tend to connect to others that are dissimilar with respect to a chosen attribute, most commonly degree. In degree disassortativity, the degrees of the two ends of a randomly chosen edge are negatively correlated. The standard quantitative measure is the assortativity coefficient r, introduced by Newman, which equals the Pearson correlation coefficient of the degrees at the ends of edges. Values of r range from -1 to 1; r < 0 indicates disassortative mixing, r > 0 indicates assortative mixing, and r ≈ 0 indicates little or no correlation.

Many social networks are assortative, with high-degree nodes tending to connect to other high-degree nodes. In contrast, many biological, technological, and ecological networks exhibit disassortativity, meaning high-degree nodes tend to connect to low-degree nodes. This pattern influences how networks grow and how flows or signals propagate through them, and it can affect robustness to failures or targeted disruptions. For example, hub nodes connected to many low-degree neighbors can shape the spread of information or disease and the network’s vulnerability to attacks that focus on high-degree nodes.

Beyond degree, mixing patterns can also be analyzed in terms of other node attributes, using mixing matrices or joint distributions to describe tendencies for categories such as function, type, or other features. Disassortativity is thus a descriptive property of network structure that helps explain and anticipate the behavior of dynamical processes occurring on networks.