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barbell_graph¶
- barbell_graph(m1, m2, create_using=None)[source]¶
Return 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 etext on Random Walks on Graphs.