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GraphTheory

  

IsNetwork

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IsNetwork(G, s, t)

IsNetwork(G)

Parameters

G

-

directed graph

s

-

vertex

t

-

vertex

Description

• 

A network is a connected directed graph with at least one vertex with indegree 0 (the source) and at least one vertex with outdegree 0 (the sink). Note that under this definition a network may have an internal cycle.

• 

IsNetwork('G','s','t') outputs true if the directed graph G is a network with s as the source and t as the sink, and false otherwise.

• 

IsNetwork('G') tests if a directed graph is a network. The output is a sequence of two sets of vertices, sources and sinks, of all possible sources and sinks.  If these sets are both empty then G is implicitly not a network.

Examples

withGraphTheory:

NDigraph1,2,1,3,2,4,3,4

NGraph 1: a directed unweighted graph with 4 vertices and 4 arc(s)

(1)

IsNetworkN

1,4

(2)

IsNetworkN,1,4

true

(3)

IsNetworkN,1,2

false

(4)

DrawNetworkN

See Also

Digraph

DrawNetwork

MaxFlow

RandomGraphs[RandomNetwork]