NetworkFlow[g,source,sink]
returns the value of a maximum flow through graph g from source to sink.
NetworkFlow[g,source,sink,Edge]
returns the edges in g that have positive flow, along with their flows, in a maximum flow from source to sink.
NetworkFlow[g,source,sink,Cut]
returns a minimum cut between source and sink.
NetworkFlow[g,source,sink,All]
returns the adjacency list of g along with flows on each edge in a maximum flow from source to sink.


NetworkFlow
NetworkFlow[g,source,sink]
returns the value of a maximum flow through graph g from source to sink.
NetworkFlow[g,source,sink,Edge]
returns the edges in g that have positive flow, along with their flows, in a maximum flow from source to sink.
NetworkFlow[g,source,sink,Cut]
returns a minimum cut between source and sink.
NetworkFlow[g,source,sink,All]
returns the adjacency list of g along with flows on each edge in a maximum flow from source to sink.
Details and Options
- NetworkFlow functionality is now available in the built-in Wolfram Language function FindMaximumFlow.
- To use NetworkFlow, you first need to load the Combinatorica Package using Needs["Combinatorica`"].
- The graph g can be a directed or an undirected graph.
Examples
Basic Examples (2)
NetworkFlow has been superseded by FindMaximumFlow:
Tech Notes
Related Guides
-
▪
- Combinatorica Package ▪
- Graph Algorithms ▪
- Graphs & Networks ▪
- Graph Visualization ▪
- Computation on Graphs ▪
- Graph Construction & Representation ▪
- Graphs and Matrices ▪
- Graph Properties & Measurements ▪
- Graph Operations and Modifications ▪
- Statistical Analysis ▪
- Social Network Analysis ▪
- Graph Properties ▪
- Mathematical Data Formats ▪
- Discrete Mathematics
Text
Wolfram Research (2012), NetworkFlow, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/NetworkFlow.html.
CMS
Wolfram Language. 2012. "NetworkFlow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/Combinatorica/ref/NetworkFlow.html.
APA
Wolfram Language. (2012). NetworkFlow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/Combinatorica/ref/NetworkFlow.html
BibTeX
@misc{reference.wolfram_2025_networkflow, author="Wolfram Research", title="{NetworkFlow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/Combinatorica/ref/NetworkFlow.html}", note=[Accessed: 13-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_networkflow, organization={Wolfram Research}, title={NetworkFlow}, year={2012}, url={https://reference.wolfram.com/language/Combinatorica/ref/NetworkFlow.html}, note=[Accessed: 13-August-2025]}