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.
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.
References
Newman, M.E.J. (2003). Mixing patterns in networks. Physical Review E, 67(2), 026126. doi:10.1103/PhysRevE.67.026126
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