Simple graphs are graphs which do not contain loop and multiple edges.

## Usage

```
simplify(
graph,
remove.multiple = TRUE,
remove.loops = TRUE,
edge.attr.comb = igraph_opt("edge.attr.comb")
)
is_simple(graph)
simplify_and_colorize(graph)
```

## Arguments

- graph
The graph to work on.

- remove.multiple
Logical, whether the multiple edges are to be removed.

- remove.loops
Logical, whether the loop edges are to be removed.

- edge.attr.comb
Specifies what to do with edge attributes, if

`remove.multiple=TRUE`

. In this case many edges might be mapped to a single one in the new graph, and their attributes are combined. Please see`attribute.combination()`

for details on this.

## Details

A loop edge is an edge for which the two endpoints are the same vertex. Two edges are multiple edges if they have exactly the same two endpoints (for directed graphs order does matter). A graph is simple is it does not contain loop edges and multiple edges.

`is_simple()`

checks whether a graph is simple.

`simplify()`

removes the loop and/or multiple edges from a graph. If
both `remove.loops`

and `remove.multiple`

are `TRUE`

the
function returns a simple graph.

`simplify_and_colorize()`

constructs a new, simple graph from a graph and
also sets a `color`

attribute on both the vertices and the edges.
The colors of the vertices represent the number of self-loops that were
originally incident on them, while the colors of the edges represent the
multiplicities of the same edges in the original graph. This allows one to
take into account the edge multiplicities and the number of loop edges in
the VF2 isomorphism algorithm. Other graph, vertex and edge attributes from
the original graph are discarded as the primary purpose of this function is
to facilitate the usage of multigraphs with the VF2 algorithm.

## See also

`which_loop()`

, `which_multiple()`

and
`count_multiple()`

, `delete_edges()`

,
`delete_vertices()`

Other functions for manipulating graph structure:
`+.igraph()`

,
`add_edges()`

,
`add_vertices()`

,
`complementer()`

,
`compose()`

,
`connect()`

,
`contract()`

,
`delete_edges()`

,
`delete_vertices()`

,
`difference.igraph()`

,
`difference()`

,
`disjoint_union()`

,
`edge()`

,
`igraph-minus`

,
`intersection.igraph()`

,
`intersection()`

,
`path()`

,
`permute()`

,
`rep.igraph()`

,
`reverse_edges()`

,
`union.igraph()`

,
`union()`

,
`vertex()`

Other functions for manipulating graph structure:
`+.igraph()`

,
`add_edges()`

,
`add_vertices()`

,
`complementer()`

,
`compose()`

,
`connect()`

,
`contract()`

,
`delete_edges()`

,
`delete_vertices()`

,
`difference.igraph()`

,
`difference()`

,
`disjoint_union()`

,
`edge()`

,
`igraph-minus`

,
`intersection.igraph()`

,
`intersection()`

,
`path()`

,
`permute()`

,
`rep.igraph()`

,
`reverse_edges()`

,
`union.igraph()`

,
`union()`

,
`vertex()`

Other functions for manipulating graph structure:
`+.igraph()`

,
`add_edges()`

,
`add_vertices()`

,
`complementer()`

,
`compose()`

,
`connect()`

,
`contract()`

,
`delete_edges()`

,
`delete_vertices()`

,
`difference.igraph()`

,
`difference()`

,
`disjoint_union()`

,
`edge()`

,
`igraph-minus`

,
`intersection.igraph()`

,
`intersection()`

,
`path()`

,
`permute()`

,
`rep.igraph()`

,
`reverse_edges()`

,
`union.igraph()`

,
`union()`

,
`vertex()`

## Author

Gabor Csardi csardi.gabor@gmail.com

## Examples

```
g <- make_graph(c(1, 2, 1, 2, 3, 3))
is_simple(g)
#> [1] FALSE
is_simple(simplify(g, remove.loops = FALSE))
#> [1] FALSE
is_simple(simplify(g, remove.multiple = FALSE))
#> [1] FALSE
is_simple(simplify(g))
#> [1] TRUE
```