lollipop_graph¶

lollipop_graph(m, n, create_using=None)[source]¶

Return the Lollipop Graph; K_m connected to P_n.

This is the Barbell Graph without the right barbell.

Parameters:

m, n (int or iterable container of nodes (default = 0)) – If an integer, nodes are from range(m) and range(m,m+n). If a container, the entries are the coordinate of the node.

The nodes for m appear in the complete graph K_m and the nodes for n appear in the path P_n
create_using (Graph, optional (default Graph())) – If provided this graph is cleared of nodes and edges and filled with the new graph. Usually used to set the type of the graph.

Notes

The 2 subgraphs are joined via an edge (m-1, m). If n=0, this is merely a complete graph.

(This graph is an extremal example in David Aldous and Jim Fill’s etext on Random Walks on Graphs.)