# a1rk: Rank of the A-1 homotopy group of a graph In corybrunson/atheory: A-theory

## Description

Calculate the rank (the number of homotopy-inequivalent cycles) of the first discrete homotopy group of a graph.

## Usage

 `1` ```a1rk(graph, componentwise = FALSE) ```

## Arguments

 `graph` The input graph. It will be treated as simple and undirected. A submodule handles the case that `graph` is connected, and a wrapper feeds this submodule the connected components of `graph`. `componentwise` Logical, defaults to false. If true, returns a vector of the A-1 ranks of the connected components of `graph`. If false, returns the A-1 rank of `graph`, which is the sum of these ranks.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# cycle graph g <- graph(c(1,2, 2,3, 3,4, 4,5, 5,1), directed = FALSE) a1rk(g) # two-cycle graph h <- add_vertices(g, 4) h <- add_edges(h, c(2,6, 6,7, 7,8, 8,9, 9,1)) a1rk(h) # Platonic solids a1rk(graph.famous("tetrahedron")) a1rk(graph.famous("cubical")) a1rk(graph.famous("dodecahedron")) ```

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