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.

(Source code, png)

m, nint or iterable container of nodes

If an integer, nodes are from range(m) and range(m, m+n). If a container of nodes, those nodes appear in the graph. Warning: m and n are not checked for duplicates and if present the resulting graph may not be as desired. Make sure you have no duplicates.

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.

Networkx graph

A complete graph with m nodes connected to a path of length n.


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.)

Additional backends implement this function

cugraph : GPU-accelerated backend.