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Q-Analysis

Source: R/simplicial.R
q_analysis.Rd

Computes Q-connectivity structure (Atkin 1974). Two maximal simplices are q-connected if they share a face of dimension \(\geq q\). Reports:

  • Q-vector: number of connected components at each q-level

  • Structure vector: highest simplex dimension per node

Usage

q_analysis(sc)

# S3 method for class 'q_analysis'
print(x, ...)

# S3 method for class 'q_analysis'
plot(x, combined = TRUE, ...)

Arguments

sc

A simplicial_complex object.

x

For the print() and plot() methods: an object of class q_analysis.

...

In plot.q_analysis(): Ignored. In print.q_analysis(): Additional arguments (unused).

combined

When TRUE (default), the two panels are stitched side-by-side via gridExtra::arrangeGrob. When FALSE, returns a named list (q_vector, structure_vector) of ggplots.

Value

A q_analysis object with $q_vector, $structure_vector, and $max_q.

In print.q_analysis(): The input object, invisibly.

In plot.q_analysis(): A grid grob (invisibly) when combined = TRUE; a named list of two ggplots when combined = FALSE.

Methods

  • plot.q_analysis(): Two panels: Q-vector (components at each connectivity level) and structure vector (max simplex dimension per node).

References

Atkin, R. H. (1974). Mathematical Structure in Human Affairs.

Examples

mat <- matrix(c(0,.6,.5,.6,0,.4,.5,.4,0), 3, 3)
colnames(mat) <- rownames(mat) <- c("A","B","C")
sc <- build_simplicial(mat, threshold = 0.3)
q_analysis(sc)
#> Q-Analysis (max q = 2)
#>   Components: q2:1 q1:1 q0:1
#>   Fully connected at all q levels
#>   Structure: A:2 B:2 C:2