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 whose names cover every node name, or an unnamed vector of length equal to the number of nodes, in node order. A numeric vector is treated as scalar and any other vector as nominal.
- directed
Logical or NULL. If NULL (default), auto-detect.
- digits
Integer or NULL. Round the coefficient to this many decimal places. Default NULL (no rounding).
- ...
Not used. Any argument supplied here raises an
"unused argument"error.
Value
An object of class "cograph_assortativity" with components:
- coefficient
Numeric scalar: assortativity coefficient.
- type
Character:
"nominal"or"scalar".- directed
Logical: whether the network was treated as directed.
- n_nodes
Numeric: number of nodes.
- n_edges
Numeric: number of edges.
- attribute_values
The attribute values used, named by node and in node order.
- network
The original input network.
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