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