Author: Mark Ortmann

# Introduction to oaqc

#### Mark Ortmann

# 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

## Input

The input can either be an edgelist (matrix or data.frame) or a 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 = FALSE, 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