degreedisassortative

Degree disassortativity, or degree disassortativity, is a network property describing a tendency for nodes to connect to others with different degrees. In a disassortative network, high-degree nodes are more likely to connect to low-degree nodes, and vice versa, yielding a negative correlation between the degrees of adjacent nodes.

Measurement and interpretation

The degree assortativity of a network is commonly summarized by the degree assortativity coefficient, r, which is the Pearson correlation coefficient of the degrees at the two ends of each edge. Values of r range from -1 to 1: negative values indicate disassortativity, positive values indicate assortativity (preference for similar degrees), and values near zero indicate no strong degree-based mixing pattern. r is computed from the network’s degree sequence and edge connections, without requiring the specific identity of nodes.

Contexts and implications

Degree disassortativity is observed in several real-world networks, notably many technological and biological systems. For example, the internet’s router or autonomous systems topology and various protein interaction or metabolic networks often display disassortative mixing. Disassortativity can influence network dynamics and resilience: connections between hubs and many low-degree nodes can affect how processes such as information diffusion, epidemic spread, or targeted attacks propagate and how robust the network is to failures.

Causes and variation

Disassortativity can arise from organizational or developmental constraints, optimization for efficiency, or hierarchical structures that favor hub-to-periphery connections. Not all networks are disassortative; some social or collaboration networks show weak or positive degree correlations, reflecting different underlying formation mechanisms.

See also

Assortativity, degree correlations, network topology, complex networks.