The nodal distribution of a given standard quantum graph have been shown to hold information about the topology of the graph, and it was explicitly calculated for specific families of graphs. In all of those cases, and in any numerical simulation, the nodal distribution appears to converge to a Gaussian distribution as the number of edges (more specifically, the first Betti number) goes to infinity. We conjecture that the convergence of the nodal distribution to Gaussian distribution is a universl property of quantum graphs. We have proved the convergence for several families of graphs.