Degree Assortativity Coefficient

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.

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.

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.

References

Newman, M.E.J. (2002). Assortative mixing in networks. Physical Review Letters, 89(20), 208701. doi:10.1103/PhysRevLett.89.208701

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)
#> Assortativity (Degree)
#> =================================== 
#>   Coefficient: -0.1667 
#>   Interpretation: disassortative 
#>   Nodes: 5   Edges: 7 
#>   Directed: FALSE