graphscope.nx.generators.classic.barbell_graph

graphscope.nx.generators.classic.barbell_graph(m1, m2, create_using=None)

Returns the Barbell Graph: two complete graphs connected by a path.

For $m1 > 1$ and $m2 >= 0$.

Two identical complete graphs $K_{m1}$ form the left and right bells, and are connected by a path $P_{m2}$.

The 2*m1+m2 nodes are numbered

0, …, m1-1 for the left barbell, m1, …, m1+m2-1 for the path, and m1+m2, …, 2*m1+m2-1 for the right barbell.

The 3 subgraphs are joined via the edges (m1-1, m1) and (m1+m2-1, m1+m2). If m2=0, this is merely two complete graphs joined together.

This graph is an extremal example in David Aldous and Jim Fill’s e-text on Random Walks on Graphs.