function max_flow = ford_fulkerson(G, s, t)
    % G is a weighted adjacency matrix representing the graph
    % s is the source node
    % t is the sink node

    % Initialize the maximum flow to 0
    max_flow = 0;

    % Initialize the residual graph to be the same as the original graph
    R = G;

    % While there is a path from s to t in the residual graph
    while true
        % Find a path from s to t in the residual graph using depth-first search
        path = depth_first_search(R, s, t);
        
        % If no path was found, break out of the loop
        if isempty(path)
            break;
        end

        % Find the minimum weight along the path
        min_weight = min(R(path(1:end-1), path(2:end)));

        % Add the minimum weight to the maximum flow
        max_flow = max_flow + min_weight;

        % Update the residual graph
        for i = 1:length(path)-1
            R(path(i), path(i+1)) = R(path(i), path(i+1)) - min_weight;
            R(path(i+1), path(i)) = R(path(i+1), path(i)) + min_weight;
        end
    end
end

function path = depth_first_search(G, s, t)
    % G is a weighted adjacency matrix representing the graph
    % s is the source node
    % t is the sink node

    % Initialize a stack and a visited array
    stack = s;
    visited = zeros(size(G, 1), 1);

    % Initialize the path to be empty
    path = [];

    % While the stack is not empty
    while ~isempty(stack)
        % Pop the top element from the stack
        v = stack(end);
        stack(end) = [];

        % If the element has not been visited
        if ~visited(v)
            % Mark the element as visited
            visited(v) = 1;

            % If the element is the sink, break out of the loop
            if v == t
                break;
            end

            % Add the element to the path
            path = [path, v];

            % Find the neighbors of the element
            neighbors = find(G(v, :) > 0);

            % Push the neighbors onto the stack
            stack = [stack, neighbors];
        end
    end
end