To create a graph you can look into this documentation Graphs in MATLAB
This is how you can compute for the matrix of the distance of the paths among all the nodes:
G = graph(); % Create a graph
G = addnode(G, 5); % Add 5 nodes to the graph
G = addedge(G, [1 1 2 2 3 4], [2 3 3 4 5 5]); % Add edges to the graph
Distances(G, 'Method' , 'unweighted') % Compute the matrix of distances