Description Usage Arguments Examples

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.

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

`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. |

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)
``` |

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