heterogeneity {migraph}

Measures of network diversity

Description

These functions offer ways to summarise the heterogeneity of an attribute across a network, within groups of a network, or the distribution of ties across this attribute:

• network_richness() measures the number of unique categories in a network attribute.

• node_richness() measures the number of unique categories of an attribute to which each node is connected.

• network_diversity() measures the heterogeneity of ties across a network or within clusters by node attributes.

• node_diversity() measures the heterogeneity of each node's local neighbourhood.

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

• node_heterophily() measures each node's embeddedness within groups of nodes with the same attribute.

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

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

Usage

network_richness(.data, attribute)

node_richness(.data, attribute)

network_diversity(.data, attribute, clusters = NULL)

node_diversity(.data, attribute)

network_heterophily(.data, attribute)

node_heterophily(.data, attribute)

network_assortativity(.data)

network_spatial(.data, attribute)

Arguments

.data

An object of a {manynet}-consistent class:

• matrix (adjacency or incidence) from {base} R

• edgelist, a data frame from {base} R or tibble from {tibble}

• igraph, from the {igraph} package

• network, from the {network} package

• tbl_graph, from the {tidygraph} package

attribute

Name of a nodal attribute or membership vector to use as categories for the diversity measure.

clusters

A nodal cluster membership vector or name of a vertex attribute.

network_diversity

Blau's index (1977) uses a formula known also in other disciplines by other names (Gini-Simpson Index, Gini impurity, Gini's diversity index, Gibbs-Martin index, and probability of interspecific encounter (PIE)):

1 - \sum\limits_{i = 1}^k {p_i^2 }

, where p_i is the proportion of group members in ith category and k is the number of categories for an attribute of interest. This index can be interpreted as the probability that two members randomly selected from a group would be from different categories. This index finds its minimum value (0) when there is no variety, i.e. when all individuals are classified in the same category. The maximum value depends on the number of categories and whether nodes can be evenly distributed across categories.

network_homophily

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

Blau, Peter M. (1977). Inequality and heterogeneity. New York: Free Press.

Krackhardt, David and Robert N. Stern (1988). Informal networks and organizational crises: an experimental simulation. Social Psychology Quarterly 51(2), 123-140.

Moran, Patrick Alfred Pierce. 1950. "Notes on Continuous Stochastic Phenomena". Biometrika 37(1): 17-23. doi:10.2307/2332142

See Also

Other measures: between_centrality, close_centrality, closure, cohesion(), degree_centrality, eigenv_centrality, features, hierarchy, holes, net_diffusion, node_diffusion, periods

Examples

network_richness(mpn_bristol)
node_richness(mpn_bristol, "type")
marvel_friends <- manynet::to_unsigned(manynet::ison_marvel_relationships, "positive")
network_diversity(marvel_friends, "Gender")
network_diversity(marvel_friends, "Attractive")
network_diversity(marvel_friends, "Gender", "Rich")
node_diversity(marvel_friends, "Gender")
node_diversity(marvel_friends, "Attractive")
network_heterophily(marvel_friends, "Gender")
network_heterophily(marvel_friends, "Attractive")
node_heterophily(marvel_friends, "Gender")
node_heterophily(marvel_friends, "Attractive")
network_assortativity(mpn_elite_mex)
network_spatial(ison_lawfirm, "age")