Need help to improve graphviz rendering of a basic neural network - neural-network

Question

I try to use Graphviz to get a picture of the state of a basic neural network. The input layer has 14 neurons, and the output layer is only one neuron. One can choose the number of hidden layers as well as the number of neurons that lies within each layer. Usually, there is only one hidden layer. The number of neurons within this layer can be rather big though (like 1000). But, for demonstration purposes, I only need like 5 neurons (I'm aware I'll never get useful picture for hundreds of neurons). I'd like to:
Write the weight of the edge (connection) between each neuron
Modify the thickness of the edge in accordance to its weight
Maybe label each layer
About the thickness, I know I can use "penwidth". I also know about clusters, that can help bounding each layer and label them. My main problem, so far, is that there are too many edges, between the input layer (14 neurons) and the hidden layer, for Graphiz to produce a clear picture. If I add labels to display the weights of connections, it's even worse. I think putting more space between my input and hidden layer could improve the readability of the rendering, but I didn't find how to do that, despite long researches.
Here is how looks like for the moment:
Current rendering of the neural network, without weights
Here is the automatically generated dot code that is behind this picture:
digraph graphname {
0.0 -> 1.0;
0.1 -> 1.0;
0.2 -> 1.0;
0.3 -> 1.0;
0.4 -> 1.0;
0.5 -> 1.0;
0.6 -> 1.0;
0.7 -> 1.0;
0.8 -> 1.0;
0.9 -> 1.0;
0.10 -> 1.0;
0.11 -> 1.0;
0.12 -> 1.0;
0.13 -> 1.0;
0.0 -> 1.1;
0.1 -> 1.1;
0.2 -> 1.1;
0.3 -> 1.1;
0.4 -> 1.1;
0.5 -> 1.1;
0.6 -> 1.1;
0.7 -> 1.1;
0.8 -> 1.1;
0.9 -> 1.1;
0.10 -> 1.1;
0.11 -> 1.1;
0.12 -> 1.1;
0.13 -> 1.1;
0.0 -> 1.2;
0.1 -> 1.2;
0.2 -> 1.2;
0.3 -> 1.2;
0.4 -> 1.2;
0.5 -> 1.2;
0.6 -> 1.2;
0.7 -> 1.2;
0.8 -> 1.2;
0.9 -> 1.2;
0.10 -> 1.2;
0.11 -> 1.2;
0.12 -> 1.2;
0.13 -> 1.2;
0.0 -> 1.3;
0.1 -> 1.3;
0.2 -> 1.3;
0.3 -> 1.3;
0.4 -> 1.3;
0.5 -> 1.3;
0.6 -> 1.3;
0.7 -> 1.3;
0.8 -> 1.3;
0.9 -> 1.3;
0.10 -> 1.3;
0.11 -> 1.3;
0.12 -> 1.3;
0.13 -> 1.3;
0.0 -> 1.4;
0.1 -> 1.4;
0.2 -> 1.4;
0.3 -> 1.4;
0.4 -> 1.4;
0.5 -> 1.4;
0.6 -> 1.4;
0.7 -> 1.4;
0.8 -> 1.4;
0.9 -> 1.4;
0.10 -> 1.4;
0.11 -> 1.4;
0.12 -> 1.4;
0.13 -> 1.4;
1.0 -> 2.0;
1.1 -> 2.0;
1.2 -> 2.0;
1.3 -> 2.0;
1.4 -> 2.0;
}
In this code, the neurons are numbered this way: LAYER_NUMBER.NEURON_NUMBER.
Notice that neurons do not appear in the right order in the picture, problem that I didn't solve either...
Thanks for you help.

Answer 1

Here is a graph containing a few different ideas:
ranksep increases the distance between "ranks".
margin makes nodes bigger. (There are probably better ways to do this.)
Color each node and have each edges from that node all use the same hue. For readability, you can make the nodes lighter and the edges darker versions of that hue. Don't worry about using color names, because it supports #rrggbb notation.
I've found using color like this greatly adds to visual clarity for complicated graphs. It is much easier to follow an edge when it is colored, and if something has low weight, it could be made either barely visible or completely invisible.
Another added benefit of this colorization is that it can echo the approach of staining real neurons. See this for inspiration http://neuroimages.tumblr.com
digraph graphname {
graph [rankdir="LR" ranksep="3.0"]
node [style=filled];
edge [penwidth="0.5" color="#e0e0e0"];
0.1 [fillcolor="cadetblue"];
0.2 [fillcolor="coral"];
0.3 [fillcolor="green"];
0.4 [fillcolor="gold"];
0.6 [fillcolor="cyan"];
1.0 [margin=0.4];
1.1 [margin=0.4];
1.2 [margin=0.4];
1.3 [margin=0.4];
1.4 [margin=0.4];
0.0 -> 1.0;
0.1 -> 1.0 [color="cadetblue1" penwidth="1"];
0.2 -> 1.0 [color="coral2" penwidth="2"];
0.3 -> 1.0 [color="green3" penwidth="6"];
0.4 -> 1.0 [color="gold4" penwidth="8"];
0.5 -> 1.0;
0.6 -> 1.0;
0.7 -> 1.0;
0.8 -> 1.0;
0.9 -> 1.0;
0.10 -> 1.0;
0.11 -> 1.0;
0.12 -> 1.0;
0.13 -> 1.0;
0.0 -> 1.1;
0.1 -> 1.1 [color="cadetblue2" penwidth="2"];
0.2 -> 1.1 [color="coral3" penwidth="5"];
0.3 -> 1.1 [color="green4" penwidth="8"];
0.4 -> 1.1;
0.5 -> 1.1 [color="cyan1" penwidth="1"];
0.6 -> 1.1;
0.7 -> 1.1;
0.8 -> 1.1;
0.9 -> 1.1;
0.10 -> 1.1;
0.11 -> 1.1;
0.12 -> 1.1;
0.13 -> 1.1;
0.0 -> 1.2;
0.1 -> 1.2 [color="cadetblue3" penwidth="3"];
0.2 -> 1.2 [color="coral4" penwidth="6"];
0.3 -> 1.2;
0.4 -> 1.2 [color="gold1" penwidth="1"];
0.5 -> 1.2 [color="cyan2" penwidth="2"];
0.6 -> 1.2;
0.7 -> 1.2;
0.8 -> 1.2;
0.9 -> 1.2;
0.10 -> 1.2;
0.11 -> 1.2;
0.12 -> 1.2;
0.13 -> 1.2;
0.0 -> 1.3;
0.1 -> 1.3 [color="cadetblue4" penwidth="4"];
0.2 -> 1.3;
0.3 -> 1.3 [color="green1" penwidth="1"];
0.4 -> 1.3 [color="gold2" penwidth="2"];
0.5 -> 1.3 [color="cyan3" penwidth="3"];
0.6 -> 1.3;
0.7 -> 1.3;
0.8 -> 1.3;
0.9 -> 1.3;
0.10 -> 1.3;
0.11 -> 1.3;
0.12 -> 1.3;
0.13 -> 1.3;
0.0 -> 1.4;
0.1 -> 1.4 [color="cadetblue4" penwidth="2"];
0.2 -> 1.4 [color="coral4" penwidth="2"];
0.3 -> 1.4 [color="green4" penwidth="2"];
0.4 -> 1.4 [color="gold4" penwidth="2"];
0.5 -> 1.4 [color="cyan4" penwidth="2"];
0.6 -> 1.4;
0.7 -> 1.4;
0.8 -> 1.4;
0.9 -> 1.4;
0.10 -> 1.4;
0.11 -> 1.4;
0.12 -> 1.4;
0.13 -> 1.4;
1.0 -> 2.0;
1.1 -> 2.0;
1.2 -> 2.0;
1.3 -> 2.0;
1.4 -> 2.0;
}