lame (version 1.3.4)

gof_stats_bipartite: Goodness of fit statistics for bipartite networks

Description

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)

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.

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.

Author

Cassy Dorff, Shahryar Minhas, Tosin Salau

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

Examples

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

# Calculate GOF statistics
gof_stats_bipartite(Y)
# }