assortativity_attribute: Attribute Assortativity (Homophily)

In cograph: Analysis and Visualization of Complex Networks

Attribute Assortativity (Homophily)

Description

Computes assortativity with respect to a node attribute, measuring the tendency of nodes to connect to others with similar attribute values. For categorical attributes, this computes the modularity-based nominal assortativity. For numeric attributes, this computes the Pearson correlation between attribute values at edge endpoints.

Usage

assortativity_attribute(x, values, directed = NULL, digits = NULL, ...)

homophily(x, values, directed = NULL, digits = NULL, ...)

Arguments

x	Network input: matrix, igraph, network, cograph_network, or tna object.
values	Named vector of attribute values (names must match node names) or an unnamed vector in node order.
directed	Logical or NULL. If NULL (default), auto-detect.
digits	Integer or NULL. Round result. Default NULL.
...	Additional arguments passed to to_igraph.

Details

For categorical (nominal) attributes, the coefficient is:

r = \frac{\text{tr}(\mathbf{e}) - \|\mathbf{e}^2\|}{1 - \|\mathbf{e}^2\|}

where \mathbf{e} is the mixing matrix with e_{ij} = fraction of edges connecting type i to type j.

For numeric (scalar) attributes, the coefficient is the Pearson correlation between attribute values at edge endpoints.

Value

An object of class "cograph_assortativity" with components:

coefficient

Numeric scalar: assortativity coefficient.

type

Character: "nominal" or "scalar".

directed

Logical.

n_nodes

Integer.

n_edges

Integer.

attribute_values

The attribute values used.

network

Original input.

References

Newman, M.E.J. (2003). Mixing patterns in networks. Physical Review E, 67(2), 026126. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1103/PhysRevE.67.026126")}

See Also

assortativity, detect_communities

Examples

adj <- matrix(c(0,1,1,0, 1,0,0,0, 1,0,0,1, 0,0,1,0), 4, 4)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
groups <- c(A = "x", B = "x", C = "y", D = "y")
cograph::assortativity_attribute(adj, groups)

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