# Introduction to oaqc

This package provides an efficient algorithm to calculate for a given graph the **o**rbit-**a**ware **q**uad **c**ensus. 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.

## Input

The input can either be

- Edge-List (matrix or data.frame)
- Graph Object ('igraph')

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.

```
library(oaqc)
### 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.

## Result

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

```
print(k4orbits$n_orbits_ind[,10])
```

```
## [1] 0 0 0 0
```