We've already seen ring graphs, a ring is a connected graph in which each vertex is connected to exactly two other vertices. tkigraph can generate rings of different sizes, choose “Ring” from the “Create” menu.

For creating a ring in tkigraph, choose the “Ring” command from the “Create” menu. The only parameter you can set is the number of vertices.

A lattice is a graph in which the vertices are placed on a grid and the neighboring vertices are connected by an edge. A one dimensional lattice is like a ring, only it is not circular, the circle is not closed. A two dimensional lattice can be seen in the following picture:

In tkigraph a lattice can be created by choosing “Lattice” from the “Create” menu. You can set the dimension of the lattice and also the size along the dimensions. Eg. if you set “Dimensions” to 2 and “Size 1” and “Size 2” to 10 and 5, then you will get a two-dimensional 10x5 lattice. The other “Size” parameters are ignored.

A tree is a connected graph which contains no circles. A tree graph is usually plotted “tree-like” with its root on the top and then its branches going downward. (Hence its name.) The top vertex is called the “root” and the vertices at the next lower level are called the children of the root. In general the neighbors of a vertex at a lower level are called the children of that vertex.

igraph can only create regular trees, in which (almost) every vertex has the same number of children. An example is show in the following picture.

Here (almost) every vertex has two children, the children of vertex 0 are vertex 1 and 2, the children of vertex 5 are vertex 11 and 12.

A tree can be created in tkigraph by choosing “Tree” from the “Create” menu. The number of vertices in the tree can be given and also the number of children at each non-terminal vertex. Three different types of graphs can be created: undirected, directed where the edges point from the root to the children, or the opposite.

A star graph is a special tree, where every vertex is connected to the root. There are three kinds of star graphs in tkigraph just like there are three types of trees.

In a full graph every possible edge is realized, ie. there is an edge between every pair of vertices.

In tkigraph a full graph can be created by choosing “Full” from the “Create” menu. Be careful with this function, do not try to create very big full graphs. If you have a full graph with 1000 vertices that will contain at least 499500 edges which is fine (until you want to plot it), but 10000 vertices means about 50 million edges and while this is not a problem for the igraph software, your PC probably does not have enough memory to handle this amount of data.

The graph atlas is a book containing all undirected graphs with up to seven vertices. (“An Atlas of Graphs” by Ronald C. Read and Robin J. Wilson, Oxford University Press, 1998.) Each graph in the atlas has a numeric id between 0 and 1252. You can see all graphs at this page. If you want to create a graph with some specific structure, just use its id in tkigraph after choosing “Graph atlas” from the “Create” menu.