# Shortest path from 1 to n

**shortest**

**path**problem is the problem of finding a

**path**between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.. The problem of finding the

**shortest**

**path**between two intersections on a road map may be modeled as a special case of the

**shortest**

**path**problem in graphs, where the vertices correspond to intersections and.

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**N**

**shortest**

**path**between two nodes. As example, the following code create three nodes and four edges, and the two

**shortest**

**paths**are (

**1**, 3) and (

**1**, 2, 3) import networkx as nx G.

**shortest**

**path**problem for a graph with non-negative edge

**path**costs, producing a

**shortest**

**path**tree.. This algorithm is often used in routing and as a subroutine in other graph algorithms.. For a given source vertex (node) in the.

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**shortest path**from node

**1**to node 6 is

**path**= [

**1**5 4 6] and pred = [0 6 5 5

**1**4]. Now you can determine the

**shortest paths**from node

**1**to any other node within the graph by indexing into pred. For example, to figure out the

**shortest path**from node

**1**to node 2, you can query pred with the destination node as the first. The

**Shortest**root from the source.

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**1**-6. Suppose we also wish to compute the vertices on

**shortest paths**in the algorithms of this section. Show how to compute the predecessor matrix. ∏. \prod ∏ from the completed matrix. L. L L of

**shortest**-

**path**weights in. O (

**n**3) O (

**n**^3) O(n3) time.