The edge connectivity of an undirected graph represents the minimum number of edges that need to be removed in order to disconnect the graph. There are several algorithms that can be used to compute the edge connectivity of an undirected graph, such as the Ford-Fulkerson algorithm and the Stoer-Wagner algorithm.
In MATLAB, you can use the graphminspantree function from the MATLAB Graph and Network Algorithms Toolbox to compute the edge connectivity of an undirected graph. This function calculates the minimum spanning tree of the graph and returns the total weight of the edges in the tree. The edge connectivity of the graph is equal to the weight of the minimum spanning tree minus one.
Here's an example:
G = graph([1 1 2 2 3 4 4 5], [2 3 3 4 5 5 6 6]); % Create an undirected graph
MST = graphminspantree(G); % Compute the minimum spanning tree and edge connectivity
edgeConnectivity = sum(MST.Edges.Weight) - 1;
disp(edgeConnectivity); % Display the edge connectivity
In this example, the graph function is used to create an undirected graph G with some edges. The graphminspantree function is then applied to compute the minimum spanning tree MST of the graph. Finally, the edge connectivity is calculated as the sum of the weights of the edges in the minimum spanning tree minus one.
Please note that the Graph and Network Algorithms Toolbox is required to use the graphminspantree function in MATLAB.
