Visualizing graph-based data (i.e., network) I'm fascinated by the concept of graph, be it the social network, the book-topic relationship and others. By graph I mean something like this:

I want to know, how to visualize the data, and is there any mathmatical background/properties behind it? Speficially, I want to know:


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*How is the graph data layed out? How the distance between different nodes is determined?

*Is there any good book on this topic?

*Any good example on applying the graph visualization?

I find some good links to start with:


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*http://www.datavizcatalogue.com/methods/network_diagram.html, tools to create graphs

*http://www.cs.umd.edu/hcil/graphvis/, tools to create graphs

*http://kateto.net/network-visualization, R introduction on graph, very detailed

*Gephi, Neo4j

*www.yasiv.com, Amazon book graph visualization
 A: Graph visualization is an entire field of study, and a vast one. What algorithm you want to use to layout your graph depends on the structure of your graph (is it sparse, small, bipartite, a tree, etc.), on any other structure present (in your example, some nodes are emphasized), on whether you want to emphasize certain aspects and so forth.
One professor I used to study under is Dorothea Wagner. One possibility for you would be to take a look at any courses she or her group offer and at the suggested reading, e.g., here. Or you may want to look at Drawing Graphs by Kaufmann and Wagner. I personally liked Graph Drawing: Algorithms for the Visualization of Graphs (Di Battista et al., 1999) back in my younger days, but this may be dated by now.
Finally, this is not really a statistical question. You might get better answers at Programmers.SE or Computer Graphics.SE or CS.SE, though a quick look at their tags didn't turn up anything.
A: Network data is all about statistics. There are node level statistics (describing individual points within the graph) such as degree centrality, and graph-level statistics which describe the overall network, such as average distance between nodes, density, and fragmentation. 
https://www.amazon.com/Statistical-Analysis-Network-Data-Statistics/dp/038788145X
