GRAPH UTILITIES PACKAGE SYMBOL

GraphDistance

gives the distance from vertex i to vertex j in the graph g.

MORE INFORMATION

To use , you first need to load the Graph Utilities Package using .

returns the graph distance from one vertex to another. Infinity is returned if no path exists from i to j. By default every edge is assumed to have an edge weight of 1.

The following option can be used:

Weighted

False

specifies whether edge weight is to be used in calculating distance

EXAMPLES

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Basic Examples (1)

This defines a simple directed graph:

This calculates the distance from vertex 1 to vertex 5:

There is no path from vertex 4 to vertex 1:

This defines a simple directed graph with edge weights:

This shows that the distance from vertex 1 to 3 is 2 if unit edge weights are assumed:

But the distance becomes 0 if edge weights are taken into account:

Needs["GraphUtilities`"]

This defines a simple directed graph:

In[2]:=

In[3]:=

Out[3]=

This calculates the distance from vertex 1 to vertex 5:

In[4]:=

Out[4]=

There is no path from vertex 4 to vertex 1:

In[5]:=

Out[5]=

This defines a simple directed graph with edge weights:

In[6]:=

In[7]:=

Out[7]=

This shows that the distance from vertex 1 to 3 is 2 if unit edge weights are assumed:

In[8]:=

Out[8]=

But the distance becomes 0 if edge weights are taken into account:

In[9]:=

Out[9]=

Applications (1)

This generates a random directed graph with n nodes and degree d:

Average distance between vertices 1 and 100, of 200 random directed graphs of 100 vertices and degree 2:

The average distance decreases with an increase in the degree:

Possible Issues (1)

This defines a small directed graph:

This shows that the distance between vertices 1 and 3 is 2, assuming a unit edge weight:

This shows that when edge weights are taken into account, the distance between vertices 1 and 3 is 0:

This shows the shortest path when edge weights are taken into account:

This shows the shortest path when edge weights are ignored: