# sc_to_graph: q-connectivity graph for a simplicial complex In corybrunson/atheory: A-theory

## Description

Given a simplicial complex and a dimension q, construct the q-connectivity graph, which is the graph whose nodes are the maximal simplices of the complex and whose edges link those pairs of simplices that share a face of dimension at least q.

## Usage

 `1` ```sc_to_graph(sc, q) ```

## Arguments

 `sc` The input simplicial complex, represented as a list of simplicies, each a vector of positive integers representing the nodes. `q` A positive integer, the minimal dimension of a face two simplices must share in order to be connected.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```# This example is taken from Barcelo & Laubenbacher (2005) # http://www.sciencedirect.com/science/article/pii/S0012365X05002323 sc1 <- list( c(1,2,3), c(1,3,4), c(1,4,5), c(1,5,6), c(1,6,2) ) sc1_graph <- sc_to_graph(sc1, q = 1) a1rk(sc1_graph) # filling the combinatorial hole sc2 <- c(sc1, list(c(1,2,5))) sc2_graph <- sc_to_graph(sc2, q = 1) a1rk(sc2_graph) ```

corybrunson/atheory documentation built on May 13, 2019, 10:51 p.m.