igraph is a library and R package for network analysis.

## Introduction

The main goals of the igraph library is to provide a set of data types and functions for 1) pain-free implementation of graph algorithms, 2) fast handling of large graphs, with millions of vertices and edges, 3) allowing rapid prototyping via high level languages like R.

## igraph graphs

igraph graphs have a class ‘`igraph`

’. They are printed to
the screen in a special format, here is an example, a ring graph
created using `make_ring()`

:

```
IGRAPH U--- 10 10 -- Ring graph
+ attr: name (g/c), mutual (g/x), circular (g/x)
```

‘`IGRAPH`

’ denotes that this is an igraph graph. Then
come four bits that denote the kind of the graph: the first is
‘`U`

’ for undirected and ‘`D`

’ for directed
graphs. The second is ‘`N`

’ for named graph (i.e. if the
graph has the ‘`name`

’ vertex attribute set). The third is
‘`W`

’ for weighted graphs (i.e. if the
‘`weight`

’ edge attribute is set). The fourth is
‘`B`

’ for bipartite graphs (i.e. if the
‘`type`

’ vertex attribute is set).

Then come two numbers, the number of vertices and the number of edges
in the graph, and after a double dash, the name of the graph (the
‘`name`

’ graph attribute) is printed if present. The
second line is optional and it contains all the attributes of the
graph. This graph has a ‘`name`

’ graph attribute, of type
character, and two other graph attributes called
‘`mutual`

’ and ‘`circular`

’, of a complex
type. A complex type is simply anything that is not numeric or
character. See the documentation of `print.igraph()`

for
details.

If you want to see the edges of the graph as well, then use the
`print_all()`

function:

```
> print_all(g)
IGRAPH badcafe U--- 10 10 -- Ring graph
+ attr: name (g/c), mutual (g/x), circular (g/x)
+ edges:
[1] 1-- 2 2-- 3 3-- 4 4-- 5 5-- 6 6-- 7 7-- 8 8-- 9 9--10 1--10
```

## Creating graphs

There are many functions in igraph for creating graphs, both deterministic and stochastic; stochastic graph constructors are called ‘games’.

To create small graphs with a given structure probably the
`graph_from_literal()`

function is easiest. It uses R's formula
interface, its manual page contains many examples. Another option is
`graph()`

, which takes numeric vertex ids directly.
`graph_from_atlas()`

creates graph from the Graph Atlas,
`make_graph()`

can create some special graphs.

To create graphs from field data, `graph_from_edgelist()`

,
`graph_from_data_frame()`

and `graph_from_adjacency_matrix()`

are
probably the best choices.

The igraph package includes some classic random graphs like the
Erdős-Rényi GNP and GNM graphs (`sample_gnp()`

, `sample_gnm()`

) and
some recent popular models, like preferential attachment
(`sample_pa()`

) and the small-world model
(`sample_smallworld()`

).

## Vertex and edge IDs

Vertices and edges have numerical vertex ids in igraph. Vertex ids are
always consecutive and they start with one. I.e. for a graph with
\(n\) vertices the vertex ids are between \(1\) and
\(n\). If some operation changes the number of vertices in the
graphs, e.g. a subgraph is created via `induced_subgraph()`

, then
the vertices are renumbered to satisfy this criteria.

The same is true for the edges as well, edge ids are always between one and \(m\), the total number of edges in the graph.

It is often desirable to follow vertices along a number of graph operations, and vertex ids don't allow this because of the renumbering. The solution is to assign attributes to the vertices. These are kept by all operations, if possible. See more about attributes in the next section.

## Attributes

In igraph it is possible to assign attributes to the vertices or edges
of a graph, or to the graph itself. igraph provides flexible
constructs for selecting a set of vertices or edges based on their
attribute values, see `vertex_attr()`

,
`V()`

and `E()`

for details.

Some vertex/edge/graph attributes are treated specially. One of them
is the ‘name’ attribute. This is used for printing the graph
instead of the numerical ids, if it exists. Vertex names can also be
used to specify a vector or set of vertices, in all igraph
functions. E.g. `degree()`

has a `v`

argument
that gives the vertices for which the degree is calculated. This
argument can be given as a character vector of vertex names.

Edges can also have a ‘name’ attribute, and this is treated
specially as well. Just like for vertices, edges can also be selected
based on their names, e.g. in the `delete_edges()`

and
other functions.

We note here, that vertex names can also be used to select edges.
The form ‘`from|to`

’, where ‘`from`

’ and
‘`to`

’ are vertex names, select a single, possibly
directed, edge going from ‘`from`

’ to
‘`to`

’. The two forms can also be mixed in the same edge
selector.

Other attributes define visualization parameters, see igraph.plotting for details.

Attribute values can be set to any R object, but note that storing the
graph in some file formats might result the loss of complex attribute
values. All attribute values are preserved if you use
`base::save()`

and `base::load()`

to store/retrieve your
graphs.

## Visualization

igraph provides three different ways for visualization. The first is
the `plot.igraph()`

function. (Actually you don't need to
write `plot.igraph()`

, `plot()`

is enough. This function uses
regular R graphics and can be used with any R device.

The second function is `tkplot()`

, which uses a Tk GUI for
basic interactive graph manipulation. (Tk is quite resource hungry, so
don't try this for very large graphs.)

The third way requires the `rgl`

package and uses OpenGL. See the
`rglplot()`

function for the details.

Make sure you read igraph.plotting before you start plotting your graphs.

## File formats

igraph can handle various graph file formats, usually both for reading
and writing. We suggest that you use the GraphML file format for your
graphs, except if the graphs are too big. For big graphs a simpler
format is recommended. See `read_graph()`

and
`write_graph()`

for details.

## Further information

The igraph homepage is at https://igraph.org. See especially the documentation section. Join the discussion forum at https://igraph.discourse.group if you have questions or comments.

## Author

**Maintainer**: Kirill Müller kirill@cynkra.com (ORCID)

Authors:

Gábor Csárdi csardi.gabor@gmail.com (ORCID)

Tamás Nepusz ntamas@gmail.com (ORCID)

Vincent Traag (ORCID)

Szabolcs Horvát szhorvat@gmail.com (ORCID)

Fabio Zanini fabio.zanini@unsw.edu.au (ORCID)

Daniel Noom

Other contributors:

Maëlle Salmon [contributor]

Michael Antonov [contributor]

Chan Zuckerberg Initiative [funder]