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

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

# 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.