Generating a random graph with given average(mean) degree of nodes

I want to generate a random graph (undirected without self-loop) with input average(mean) degree of nodes.

For example, with given (avg degree = 3 & n = 10), I want to have a randomly generated graph with 10 by 10 adjacency matrix and avg degree of 3.

Can anyone assit me on this please?

Answer 1

[Paras Gupta]

Hi,

I understand that you want to generate the adjacency matrix for a random undirected graph with an average degree given as input. Please refer to the code below to achieve the same.

adj = generateRandomGraph(10, 3)

adj = 10×10

0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0

G = graph(adj);

numNodes = numnodes(G)

numNodes = 10

avgDegree = mean(degree(G))

avgDegree = 3

function adjacencyMatrix = generateRandomGraph(n, avgDegree)
    % Create an empty adjacency matrix
    adjacencyMatrix = zeros(n, n);

    % Calculate the maximum number of edges allowed
    maxEdges = n * (n - 1) / 2;

    % Calculate the desired number of edges
    numEdges = round(n * avgDegree / 2);

    % Check if the desired number of edges is valid
    if numEdges > maxEdges
        error('Invalid average degree. Too high for the number of nodes.');
    end

    % Generate random edges until reaching the desired number
    while numEdges > 0
        % Generate two random nodes
        node1 = randi(n);
        node2 = randi(n);

        % Check if the edge already exists or if it's a self-loop
        if adjacencyMatrix(node1, node2) == 0 && node1 ~= node2
            % Add the edge
            adjacencyMatrix(node1, node2) = 1;
            adjacencyMatrix(node2, node1) = 1;

            % Decrease the number of remaining edges
            numEdges = numEdges - 1;
        end
    end
end

Please refer to the following documentations for more information on the functions used in the code above:

• https://www.mathworks.com/help/matlab/ref/round.html
• https://www.mathworks.com/help/matlab/ref/graph.numnodes.html
• https://www.mathworks.com/help/matlab/ref/graph.degree.html

Hope this helps.