assortativity: Degree Assortativity Coefficient

In cograph: Analysis and Visualization of Complex Networks

Degree Assortativity Coefficient

Description

Computes the degree assortativity coefficient, measuring the tendency of nodes to connect to other nodes with similar degree. Positive values indicate assortative mixing (high-degree nodes connect to high-degree nodes), negative values indicate disassortative mixing.

Usage

assortativity(x, directed = NULL, type = NULL, digits = NULL, ...)

Arguments

x	Network input: matrix, igraph, network, cograph_network, or tna object.
directed	Logical or NULL. If NULL (default), auto-detect from matrix symmetry. Set TRUE to force directed, FALSE to force undirected.
type	Character string specifying which degree correlation to compute. One of "out-in" (default for directed), "in-in", "out-out", "in-out", or "degree" (for undirected). Ignored for undirected networks.
digits	Integer or NULL. Round result to this many decimal places. Default NULL (no rounding).
...	Additional arguments passed to to_igraph.

Details

The degree assortativity coefficient is defined as the Pearson correlation coefficient between the degrees of nodes at either end of each edge (Newman 2002):

r = \frac{\sum_{jk} jk(e_{jk} - q_j q_k)}{\sigma_q^2}

where e_{jk} is the fraction of edges connecting degree-j to degree-k vertices, q_k is the excess degree distribution, and \sigma_q^2 its variance.

For directed networks, different degree combinations (in/out) at source and target ends can be specified via the type parameter.

Value

An object of class "cograph_assortativity" with components:

coefficient

Numeric scalar: the assortativity coefficient in [-1, 1].

type

Character: the degree type used.

directed

Logical: whether the network was treated as directed.

n_nodes

Integer: number of nodes.

n_edges

Integer: number of edges.

network

The original input network.

References

Newman, M.E.J. (2002). Assortative mixing in networks. Physical Review Letters, 89(20), 208701. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1103/PhysRevLett.89.208701")}

See Also

assortativity_attribute, centrality, network_summary

Examples

# Assortative network (high-degree connect to high-degree)
adj <- matrix(c(
  0, 1, 1, 1, 0,
  1, 0, 1, 1, 0,
  1, 1, 0, 0, 1,
  1, 1, 0, 0, 1,
  0, 0, 1, 1, 0
), 5, 5)
rownames(adj) <- colnames(adj) <- LETTERS[1:5]
cograph::assortativity(adj)

cograph documentation built on May 31, 2026, 5:06 p.m.