Question: consider citatations graphs in some field of research are there any known mathematical models for them ? Emperical observations on mathematical properties of such graphs (similar to mentioned below) ?
Definition: Citation graphs are graphs with vertices given by publications and edges by citations.
Here are main properties of webgraphs, I wonder about something similar for citation graphs.
1) Diameter is quite small (~6) or Law of Six degrees of separation
2) "Sparsity" - adjacency matrix is sparse matrix,
3) Power law of distribution of degrees of vertices: C/d^(2.1) - number of vertices with "d" edges
And there is suggestion for the model how webgraphs are growing: Barabási–Albert model, with the key idea of Preferential attachment:
Preferential attachment means that the more connected a node is, the more likely it is to receive new links. Nodes with higher degree have stronger ability to grab links added to the network. Intuitively, the preferential attachment can be understood if we think in terms of social networks connecting people. Here a link from A to B means that person A "knows" or "is acquainted with" person B. Heavily linked nodes represent well-known people with lots of relations.