You can accomplish this by pasting the following code into the script file generateGraph.m :-
function adjMat = generateGraph(N, D)
% Initialize an empty N*N adjacency matrix
adjMat = zeros(N);
% Generate a random spanning tree using DFS
visited = zeros(1, N);
current = 1;
stack = [];
visited(current) = 1;
while any(visited == 0)
unvisited = find(visited == 0);
next = unvisited(randi(length(unvisited)));
adjMat(current, next) = 1;
adjMat(next, current) = 1;
stack = [stack, current];
current = next;
visited(current) = 1;
while isempty(stack) == 0 && all(visited(stack) == 1)
current = stack(end);
stack(end) = [];
end
end
% Connect remaining disconnected nodes to the spanning tree, for making the graph connected
while any(visited == 0)
unvisited = find(visited == 0);
connectedNode = unvisited(randi(length(unvisited)));
existingNodes = find(visited == 1);
newNode = existingNodes(randi(length(existingNodes)));
adjMat(connectedNode, newNode) = 1;
adjMat(newNode, connectedNode) = 1;
visited(connectedNode) = 1;
end
% Keep adding edges until the desired diameter D is reached
diameter = computeDiameter(adjMat);
while diameter < D
% Randomly select two nodes that are not connected and add an edge between them. Repeat this until the diameter of the graph reaches D.
unconnectedNodes = find(sum(adjMat) < N - 1);
node1 = unconnectedNodes(randi(length(unconnectedNodes)));
node2 = unconnectedNodes(randi(length(unconnectedNodes)));
adjMat(node1, node2) = 1;
adjMat(node2, node1) = 1;
diameter = computeDiameter(adjMat);
end
end
The above script also uses a helper function computeDiameter.m to check the diameter of the graph. Here is the function:
function diameter = computeDiameter(adjMat)
% Compute the diameter of the graph using Floyd-Warshall algorithm
N = size(adjMat, 1);
distanceMatrix = adjMat;
for k = 1:N
for i = 1:N
for j = 1:N
if distanceMatrix(i, j) == 0 || (distanceMatrix(i, k) + distanceMatrix(k, j)) < distanceMatrix(i, j)
distanceMatrix(i, j) = distanceMatrix(i, k) + distanceMatrix(k, j);
end
end
end
end
diameter = max(distanceMatrix(:));
end
Hope this helps!
