Introduction to oaqc

This package provides an efficient algorithm to calculate for a given graph the orbit-aware quad census. More precisely the frequency distribution of all induced and non-induced non-isomorphic four node subgraphs, i.e. quads, on a node and edge level; see the figure below for the relation between orbit and quad.

quad census


The input can either be

Despite the input format the graph should not contain loops or multi-edges and the vertex indices have to lie in range \([0,n-1)\) with \(n\) denoting the number of vertices in the graph. Note that if the smallest index is \(1\) the algorithm will create an isolated vertex with index \(0\).

Calculating the orbit-aware quad census

The following code exemplifies the use of this package.

### k4, pure R
k4 <- data.frame(
    source = c(0, 0, 0, 1, 1, 2),
    target = c(1, 2, 3, 2, 3, 3)
k4orbits <- oaqc(k4, non_ind_freq = F, file = "")
# print(k4orbits)

In order to calculate the non-induced frequencies as well just set the corresponding flag to TRUE.

Since the orbit-aware frequencies can be rather large integers, which can cause some problems with R, the results can be directly written to a file.


The results of the, e.g., induced frequencies of the nodes in orbit 10 can be accessed in the following way.

## [1] 0 0 0 0