def degree_assortativity_coefficient(G, x='out', y='in', weight=None, nodes=None): """Compute degree assortativity of graph. Assortativity measures the similarity of connections in the graph with respect to the node degree. Parameters ---------- G : NetworkX graph x: string ('in','out') The degree type for source node (directed graphs only). y: string ('in','out') The degree type for target node (directed graphs only). weight: string or None, optional (default=None) The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node. nodes: list or iterable (optional) Compute degree assortativity only for nodes in container. The default is all nodes. Returns ------- r : float Assortativity of graph by degree. Examples -------- >>> G=nx.path_graph(4) >>> r=nx.degree_assortativity_coefficient(G) >>> print("%3.1f"%r) -0.5 See Also -------- attribute_assortativity_coefficient numeric_assortativity_coefficient neighbor_connectivity degree_mixing_dict degree_mixing_matrix Notes ----- This computes Eq. (21) in Ref. [1]_ , where e is the joint probability distribution (mixing matrix) of the degrees. If G is directed than the matrix e is the joint probability of the user-specified degree type for the source and target. References ---------- .. [1] M. E. J. Newman, Mixing patterns in networks, Physical Review E, 67 026126, 2003 .. [2] Foster, J.G., Foster, D.V., Grassberger, P. & Paczuski, M. Edge direction and the structure of networks, PNAS 107, 10815-20 (2010). """ M = degree_mixing_matrix(G, x=x, y=y, nodes=nodes, weight=weight) return numeric_ac(M)