Graph:

In this page we provide several **undirected** planar graphs, each
one with a planar embedding. Any planar graph with *n* vertices
has *m < 3n-6* edges.

To read the datasets and create new ones, please, use the following this code.

Each dataset has the following format:

<Number of vertices>

<Number of edges>

<Source vertex> <Target vertex>

<Source vertex> <Target vertex>

<Source vertex> <Target vertex>

...

<Number of edges>

<Source vertex> <Target vertex>

<Source vertex> <Target vertex>

<Source vertex> <Target vertex>

...

For each vertex *v*, the edges of *v* are listed in
counterclockwise order. All the vertices are identified by an
index. All the indices belongs to the range *[0,n-1]*, where *n*
is the number of vertices of the graph. Below, there is an example of the
format.

Graph:

Format:

5

7

0 1

0 2

0 3

0 4

1 0

1 4

1 2

2 0

2 1

3 0

3 4

4 0

4 3

4 1

7

0 1

0 2

0 3

0 4

1 0

1 4

1 2

2 0

2 1

3 0

3 4

4 0

4 3

4 1

Each dataset was generated in three stages: In the first stage, we used
the
function rnorm of R to generate random
coordinates *(x,y)* (with mean 0 and standard deviation
10,000). The only exception was the dataset World cities, which
corresponds to the coordinates of 2,243,467 uniques cities in the
world. In the second stage, we generated the Delaunay Triangulation of
the coordinates generated in the first stage. The triangulations were
generated using Triangle (with options -cezCBVPNE), a
piece of software dedicated to the generation of meshes and
triangulations. In the third stage, we generated planar embeddings of
the Delaunay triangulations computed in the second stage. The planar
embedding was generated with
the The Edge Addition
Planarity Suite (with options -s -q -p).

A planar graph with 1,000,000 vertices and 2,999,978 edges. The embedding of the graph is planar.

A planar graph with 5,000,000 vertices and 14,999,983 edges. The embedding of the graph is planar.

A planar graph with 10,000,000 vertices and 29,999,979 edges. The embedding of the graph is planar.

A planar graph with 15,000,000 vertices and 44,999,983 edges. The embedding of the graph is planar.

A planar graph with 20,000,000 vertices and 59,999,975 edges. The embedding of the graph is planar.

A planar graph with 25,000,000 vertices and 74,999,979 edges. The embedding of the graph is planar.

A triangulated planar graph with 2,243,467 vertices and 6,730,395
edges. The embedding of the graph is planar. Each vertex corresponds to
the coordinate *(lat,lon)* of a city. The list of cities is
available at
https://www.maxmind.com/en/free-world-cities-database. The
original dataset contains 3,173,959 cities, but some of them have
the same coordinates. We selected the 2,243,467 cities with unique
coordinates to build our dataset worldcities.