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

Question

Hyunjin Chung 2022-6-10

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https://ww2.mathworks.cn/matlabcentral/answers/1738270-generating-a-random-graph-with-given-average-mean-degree-of-nodes

回答： Paras Gupta 2023-9-14

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?

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Answer 1

Paras Gupta 2023-9-14

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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