measure_assort_net: Measures of network assortativity

In netrics: Many Ways to Measure and Classify Membership for Networks, Nodes, and Ties

Measures of network assortativity

Description

These functions offer ways to measure the distribution or assortativity of ties in a network:

• net_by_heterophily() measures how embedded nodes in the network are within groups of nodes with the same attribute.

• net_by_homophily() measures how embedded nodes in the network are within groups of nodes with the same attribute, but with more options for method.

• net_by_assortativity() measures the degree assortativity in a network.

• net_by_spatial() measures the spatial association/autocorrelation (global Moran's I) in a network.

Note that for two-mode networks, homophily is calculated on the mode with the attribute of interest, and the other mode is ignored. If the attribute is present on both modes, homophily is calculated on the first mode by default, but a message is given and the user can choose to calculate homophily on the other mode instead by subsetting the attribute vector and converting the network to a one-mode network.

Usage

net_by_heterophily(.data, attribute)

net_by_homophily(
  .data,
  attribute,
  assortativity = c("ie", "ei", "yule", "geary")
)

net_by_assortativity(.data)

net_by_spatial(.data, attribute)

Arguments

.data	A network object of class mnet, igraph, tbl_graph, network, or similar. For more information on the standard coercion possible, see manynet::as_tidygraph().
attribute	Name of a nodal attribute, mark, measure, or membership vector.
assortativity	Which method to use for ⁠*_homophily()⁠. Either "ie" (negative E-I index), "ei" (E-I index), "yule" (Yule's Q), or "geary" (Geary's C). Default is "ie". The E-I index is the number of ties between (or external) nodes grouped in some mutually exclusive categories minus the number of ties within (or internal) these groups divided by the total number of ties. This value can range from 1 to -1, where 1 indicates ties only between categories/groups and -1 ties only within categories/groups. Yule's Q is a measure of association for two binary variables, calculated as: Q = \frac{ad - bc}{ad + bc} where a is the number of ties between nodes in the same category, b is the number of ties between nodes in different categories, c is the number of non-ties between nodes in the same category, and d is the number of non-ties between nodes in different categories. This value can range from -1 to 1, where 1 indicates perfect association (all ties are between nodes in the same category), -1 indicates perfect disassociation (all ties are between nodes in different categories), and 0 indicates no association. Geary's C is a measure of spatial autocorrelation, calculated as: C = \frac{(n - 1) \sum \limits_{i=1}^n \sum\limits_{j=1}^n w_{ij} (x_i - x_j)^2}{2W \sum\limits_{i=1}^n (x_i - \bar{x})^2} where n is the number of nodes, w_{ij} is the weight of the tie between nodes i and j, x_i is the attribute value of node i, \bar{x} is the mean attribute value across all nodes, and W is the sum of all tie weights. This value can range from 0 to 2, where values less than 1 indicate positive autocorrelation (similar values are more likely to be connected), values greater than 1 indicate negative autocorrelation (dissimilar values are more likely to be connected), and a value of 1 indicates no autocorrelation. If an incompatible method is chosen for the attribute type, a suitable alternative will be used instead with a message.

Value

A network_measure numeric score.

Heterophily

Given a partition of a network into a number of mutually exclusive groups then The E-I index is the number of ties between (or external) nodes grouped in some mutually exclusive categories minus the number of ties within (or internal) these groups divided by the total number of ties. This value can range from 1 to -1, where 1 indicates ties only between categories/groups and -1 ties only within categories/groups.

References

On heterophily

Krackhardt, David, and Robert N. Stern. 1988. Informal networks and organizational crises: an experimental simulation. Social Psychology Quarterly 51(2): 123-140. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2786835")}

McPherson, Miller, Lynn Smith-Lovin, and James M. Cook. 2001. "Birds of a Feather: Homophily in Social Networks". Annual Review of Sociology, 27(1): 415-444. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1146/annurev.soc.27.1.415")}

On assortativity

Newman, Mark E.J. 2002. "Assortative mixing in networks". Physical Review Letters, 89(20): 208701. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1103/physrevlett.89.208701")}

On spatial autocorrelation

Moran, Patrick Alfred Pierce. 1950. "Notes on continuous stochastic phenomena". Biometrika 37(1): 17-23. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2332142")}

See Also

Other diversity: measure_assort_node, measure_diverse_net, measure_diverse_node

Other measures: measure_assort_node, measure_breadth, measure_broker_node, measure_broker_tie, measure_brokerage, measure_central_between, measure_central_close, measure_central_degree, measure_central_eigen, measure_centralities_between, measure_centralities_close, measure_centralities_degree, measure_centralities_eigen, measure_closure, measure_closure_node, measure_cohesion, measure_core, measure_diffusion_infection, measure_diffusion_net, measure_diffusion_node, measure_diverse_net, measure_diverse_node, measure_features, measure_fragmentation, measure_hierarchy, measure_periods

Examples

marvel_friends <- to_unsigned(to_uniplex(fict_marvel, "relationship"), "positive")
net_by_heterophily(marvel_friends, "Gender")
net_by_heterophily(marvel_friends, "Attractive")
net_by_homophily(marvel_friends, "Gender")
net_by_assortativity(ison_networkers)
net_by_spatial(ison_lawfirm, "age")

netrics documentation built on July 24, 2026, 5:07 p.m.