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Goodness of fit statistics for bipartite networks

Source: R/gof_stats_bipartite.R
gof_stats_bipartite.Rd

Calculates goodness of fit statistics specifically designed for bipartite networks, evaluating degree heterogeneity and higher-order dependencies.

Usage

gof_stats_bipartite(Y, warn_square = TRUE)

Arguments

Y

a bipartite relational data matrix (nA x nB rectangular matrix) where Y\[i,j\] represents the relationship from node i in set A to node j in set B. Missing values (NA) are allowed and will be handled appropriately.

warn_square

logical; if TRUE (default) a warning is issued when Y is square (a possible unipartite matrix passed by mistake). Set FALSE for a genuinely square bipartite network.

Value

A named numeric vector containing bipartite-specific goodness-of-fit statistics:

sd.rowmean

Standard deviation of row means. Measures the heterogeneity in out-degree from set A nodes (sender effects). Higher values indicate more variation in how active A nodes are.

sd.colmean

Standard deviation of column means. Measures the heterogeneity in in-degree to set B nodes (receiver effects). Higher values indicate more variation in how popular B nodes are.

four.cycles

Count of four-cycles (also called 4-paths or squares) in the bipartite network. A four-cycle occurs when two nodes from set A (e.g., i and k) both connect to the same two nodes in set B (e.g., j and l), forming a closed path: i->j->k->l->i. This measures the tendency for pairs of A-nodes to share multiple common B-node connections, capturing a form of clustering specific to bipartite networks. High four-cycle counts indicate that connections are not random but show patterns of shared preferences or co-occurrence. For example, in a user-item network, many four-cycles suggest that users who like one item tend to also like other items that co-occur with it.

Details

For bipartite networks, reciprocity and triadic closure are not meaningful concepts since edges only exist between the two node sets. Instead, this function focuses on:

  • Degree heterogeneity in both node sets

  • Four-cycles as the simplest higher-order dependence pattern

Author

Cassy Dorff, Shahryar Minhas, Tosin Salau

Examples

# \donttest{
# Create a random bipartite network
Y <- matrix(rnorm(10*12), 10, 12)

# Calculate GOF statistics
gof_stats_bipartite(Y)
#>   sd.rowmean   sd.colmean  four.cycles 
#>    0.3782757    0.2634259 2970.0000000 
# }