Which algorithms could be used to compute the diameter of a graph?

Which algorithms could be used to compute the diameter of a graph?

One way to find the diameter is All Pairs Shortest Path (APSP) algorithm, which is based on running Breadth-First search (BFS) from all vertices and selecting the longest path as the diameter. This algorithm has the complexity of O(n 3) for the weighted graphs and O(mn) for the unweighted graphs.

How do you calculate the diameter of a graph?

The diameter of graph is the maximum distance between the pair of vertices. It can also be defined as the maximal distance between the pair of vertices. Way to solve it is to find all the paths and then find the maximum of all.

How do you find the diameter of a tree algorithm?

Quick Explanation –

1. Take any arbitary node as the root node .
2. Run dfs from that node and find the farthest node.
3. let this node be x .
4. Now run dfs from this node to the farthest away node , let this node be y.
5. now the count of all the nodes that come along the way of x and y ( including them) is the diameter of the tree.

How do you find the diameter of an unweighted graph?

Start a breadth first search from one node x, and calculate the longest distance from x to another node. Call the node y, and then start another BFS from y, and calculate the longest distance from y to another node. This second distance will be the diameter of the graph.

What is diam G in graph theory?

The maximum among all the distances between a vertex to all other vertices is considered as the diameter of the Graph G. Notation − d(G) − From all the eccentricities of the vertices in a graph, the diameter of the connected graph is the maximum of all those eccentricities.

What is a diameter of tree?

The diameter of a tree (sometimes called the width) is the number of nodes on the longest path between two end nodes.

What is a diameter of a graph?

The graph diameter of a graph is the length of the “longest shortest path” (i.e., the longest graph geodesic) between any two graph vertices , where. is a graph distance.

How do you find the diameter of a graph in C++?

How to compute directed graph diameter in C++ [duplicate]

1. convert to undirected graph (for any directedMatrix[i][j] !=
2. compute max distance for any 2 nodes ( distaceMatrix[i][j] = max distance from node i to node j; distanceMatrix[i][i] = MIN)
3. find the maxim value from the above matrix and that’s our answer.

What is the diameter of a graph?

is a graph distance. In other words, a graph’s diameter is the largest number of vertices which must be traversed in order to travel from one vertex to another when paths which backtrack, detour, or loop are excluded from consideration.

How to find the diameter of an unweighted graph using the algorithm?

The algorithm exploits the following property of unweighted graphs. Let Abe the adjacency matrix of the graph with an added self-loop for each node. Then (Ak)ijis nonzero iff d(i, j) ≤ k. We can use this fact to find the graph diameter by computing log n values of Ak.

What is the fastest way to calculate the diameter of a graph?

For a general Graph G= (V,E) there is no O (log V * (V + E)) time complexity algorithm known for computing the diameter. The current best solution is O (V*V*V), e.g., by computing all shortest Paths with Floyd Warshall’s Algorithm.

How do you solve an unweighted graph with Dijkstra’s algorithm?

One solution is to solve in O (VE) time using Bellman–Ford. If there are no negative weight cycles, then we can solve in O (E + VLogV) time using Dijkstra’s algorithm . Since the graph is unweighted, we can solve this problem in O (V + E) time.

How to find the diameter of a graph using log n values?

We can use this fact to find the graph diameter by computing log n values of Ak. Here’s how the algorithm works: let A be the adjacency matrix of the graph with an added self loop for each node. Set M0= A. While Mkcontains at least one zero, compute Mk+1= Mk2. Eventually, you find a matrix MKwith all nonzero entries.