Plotting a 3d network model using graph

I want to plot a 3 dimensional network model using the graph function.

for example

edges1 = [1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,5,6,6,6,6,6,7,8,8,8,8,10,11,11,11];
egdes2 = [2,3,4,3,4,5,6,7,8,9,4,5,6,10,11,12,7,8,10,11,13,6,8,9,11,12,14,8,9,11,13,14,11,12,13,14];
x = [0,0,0.5000,0.5000,0,0.5000,0,0.5000,0,1.0000,1.0000,1.0000,1.0000,1.0000];
y = [0,0.5000,0,0.5000,0,0.5000,1.0000,1.0000,1.0000,0,0.5000,0,1.0000,1.0000];
z = [0,0.5000,0.5000,0,1.0000,1.0000,0,0.5000,1.0000,0,0.5000,1.0000,0,1.0000];
G = graph(edges1,egdes2);
plot(G,'Xdata',x,'Ydata',y,'Zdata',z)

However, the line visualization does not give good depth percepsion, and 3d structure can only be percieved when roatating the image.

I'm looking for a way to give the edges some volume to improve visualization, without making the image too heavy to handle.

Is there a neat way to do this?

Thanks!