## 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.