Attribute Assortativity (Homophily)

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.

...

Currently unused; directed is already an explicit argument above and to_igraph accepts no others.

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.

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 (computed over both orientations of every edge when the network is undirected). Any non-numeric values vector (character or factor) is treated as nominal.

The coefficient is NA when the network has no edges, when a nominal attribute has a single category, or when either value vector has zero variance.

References

Newman, M.E.J. (2003). Mixing patterns in networks. Physical Review E, 67(2), 026126. 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)
#> Assortativity (Nominal Attribute)
#> =================================== 
#>   Coefficient: 0.3333 
#>   Interpretation: assortative 
#>   Nodes: 4   Edges: 3 
#>   Directed: FALSE