gives the flow polynomial of the graph g.


uses rules vw to specify the graph g.


  • FlowPolynomial[g,k] gives the number of nowhere-zero k-flows of g.
  • FlowPolynomial[g] gives a pure function representation of the flow polynomial of g.


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Basic Examples  (1)

The flow polynomial of a Wheel graph:

Plot the polynomial:

Scope  (6)

FlowPolynomial works with undirected graphs:

Directed graphs:


Mixed graphs:

Use rules to specify the graph:

Evaluate at specific value:

Applications  (1)

Flow polynomials for wheel graphs with vertices:

Circulant graphs with vertices and two jumps:

Properties & Relations  (3)

Use TuttePolynomial to compute FlowPolynomial:

Isomorphic graphs have the same flow polynomial:

The flow polynomial for a cycle graph is k-1:

Introduced in 2014
Updated in 2015