Construct a bipartite respondent-modality graph

Builds a two-mode (bipartite) graph where one partition of vertices represents respondents (rows of the data) and the other represents modalities (factor levels). An edge connects respondent \(i\) to modality \(V{=}l\) if row \(i\) has value \(l\) on variable \(V\).

Usage

bipartite_modality_graph(data, remove_na = TRUE, row_prefix = "r")

Arguments

data

A data frame of categorical variables.

remove_na

Logical. If TRUE (default), rows with any missing value are dropped before graph construction.

row_prefix

Character. Prefix used to name respondent-side vertices. Default "r", so respondents are labelled "r1", "r2", ....

Value

An object of class "catbipartite", a list with:

graph

An igraph undirected graph with vertex attribute type (FALSE = respondent, TRUE = modality).

modalities

Data frame describing modality-side vertices, with columns node, variable, modality.

n_rows

Number of respondent-side vertices.

n_modalities

Number of modality-side vertices.

data

The processed categorical data used to build the graph (after NA removal).

Details

Bipartite (two-mode) graphs preserve the full respondent-to-modality incidence structure. They are the unprojected counterpart of the modality co-association graph returned by build_modality_graph: projecting a catbipartite onto its modality partition yields a respondents-in-common modality network, which is a count-based co-occurrence network distinct from the chi-square / phi-filtered network produced by build_modality_graph.

The bipartite graph is the correct tool when the scientific object of interest is the raw incidence relationship between units and categories — for example, affiliation networks (persons to events), ecological surveys (sites to species), or survey data seen as respondents endorsing response levels.

The resulting graph satisfies the igraph convention for bipartite graphs: igraph::bipartite_projection(g) can be called directly to obtain either the respondent-side or the modality-side projection.

Scope. A catbipartite is a raw incidence graph; it applies no statistical filter. Edges reflect endorsement, not association. For statistically-filtered category co-association, see build_modality_graph.

See also

build_modality_graph for the chi-square / phi-filtered modality co-association graph.

Examples

df <- expand_table(Titanic)
bg <- bipartite_modality_graph(df)
bg
#> catbipartite object (respondent-modality incidence graph)
#>   Respondent nodes : 2201 
#>   Modality nodes   : 10 
#>   Edges            : 8804 
#>   Variables        : Class, Sex, Age, Survived 
summary(bg)
#> $n_rows
#> [1] 2201
#> 
#> $n_modalities
#> [1] 10
#> 
#> $n_edges
#> [1] 8804
#> 
#> $variables
#> [1] "Class"    "Sex"      "Age"      "Survived"
#> 
#> $modalities_per_variable
#> 
#>      Age    Class      Sex Survived 
#>        2        4        2        2 
#> 

# Project onto modalities: edges weighted by shared respondents
proj <- igraph::bipartite_projection(bg$graph, which = "true")