Quickly determine if a graph is connected

connected.m

function result = connected(A)
    % connected(A)
    %
    % This function takes an adjacency matrix A
    % and returns if the graph is connected.
    % 1 means connected.
    % 0 means not connected.

    % We assume that the starting result is connected.
    % In lawyer terms, the graph is connected until proven
    % not connected.
    result = 1;

    start = 1;
    n = size(A, 1);

    vertices = zeros(n, 1);
    vertices(1) = 1;

    queue = zeros(n, 1);
    head = 1;
    tail = 1;
    queue(head) = 1;

    % Begin Breadth-First Search Algorithm
    while head <= tail
        for i = 1:n
            if queue(head) ~= i & A(queue(head), i) > 0 & A(queue(head), i) ~= Inf & vertices(i) == 0
                tail = tail + 1;
                queue(tail) = i;
                vertices(i) = 1;
            end
        end

        head = head + 1;
    end

    if tail ~= n
        result = 0;
    end
end