## How to find the shortest path in a graph?

TR = shortestpathtree (G,s) returns a directed graph, TR, that contains the tree of shortest paths from source node s to all other nodes in the graph. If the graph is weighted (that is, G.Edges contains a variable Weight ), then those weights are used as the distances along the edges in the graph. Otherwise, all edge distances are taken to be 1.

## Why is the shortestpath not supported in MATLAB?

The shortestpath, shortestpathtree, and distances functions do not support undirected graphs with negative edge weights, or more generally any graph containing a negative cycle, for these reasons: A negative cycle is a path that leads from a node back to itself, with the sum of the edge weights on the path being negative.

How to find the shortest path between nodes?

In general d (i,j) is the length of the shortest path between node i and node j, and for undirected graphs this is equivalent to d (j,i). For example, find the length of the shortest path between node 1 and node 10. Create and plot a graph. Find the shortest path distances from node 1, node 2, and node 3 to all other nodes in the graph.

How to create a tree of shortest paths?

TR = shortestpathtree (G,s,t) computes the tree of shortest paths between multiple source or target nodes: s can be a single source node, and t can specify multiple target nodes. s can specify several source nodes, and t can specify a single target node.

Most of the times, the problem is defined as follows: Given a graph with V vertices (numbered from 1 to V) and E edges. Find the shortest path from a source vertex to all other vertices. If a path is not possible (which happens in case of disconnected graphs), then return -1 for those destination vertices.

### Which is the shortest path to vertex 2?

Diagrammatically the graph can be represented as below: This is a disconnected graph.For source vertex 1, the shortest path to vertex 2 and 3 is 1, and the shortest path to destination 4 and 5 is -1. In a competitive programming scenario, you code mostly to the present requirement.

### How to create an undirected graph from a source?

Start from the source vertex, assign it a distance 0 and add it in the queue Remove the first element, fetch all vertices in its adjacency list. if the distance is -1, assign it the value from the distance variable. Push the vertices in another helper queue.

Which is the source vertex of the graph?

Also, the source vertex is 1. We need to find the shortest distance to each of the remaining vertices (2, 3, 4, 5). Diagrammatically the graph can be represented as below: This is a disconnected graph.For source vertex 1, the shortest path to vertex 2 and 3 is 1, and the shortest path to destination 4 and 5 is -1.