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

Returns the Lollipop Graph; K_m connected to P_n.

This is the Barbell Graph without the right barbell.

m, nint 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_usingNetworkX graph constructor, optional (default=nx.Graph)

Graph type to create. If graph instance, then cleared before populated.


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.)