Applications are open for the ACT Applied Category Theory Research School 2018! And because arithmetic science and geometric science are connected, and support one another, the full knowledge of numbers cannot be presented without encountering some geometry, or without seeing that operating in this way on numbers is close to geometry; the method is full…
One natural way to model human networks, such as social networks, transportation networks, or the internet, is with random graphs.
This paper summarizes the foundations of random graph theory, developed by Paul Erd¨os and Alfred R´enyi in 1958, and some common
techniques used to analyze random graphs. Three more generalized
random graph models are also explored: the configuration model, the
small-world model, and the preferential attachment model. The similarity of these models to human networks is evaluated based on four
criteria: average path length, degree distribution, clustering coefficient, and static or dynamic nature of the graph.
M. Bodirsky, O. Giménez, M. Kang, and M. Noy. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), volume AE of DMTCS Proceedings, page 383---388. Discrete Mathematics and Theoretical Computer Science, (2005)
J. Dubuisson, J. Eckmann, C. Scheible, and H. Schutze. Proceedings of the 2013 Conference on Empirical Methods in Natural Language Processing, page 669-680. Seattle, Washington, USA, Association for Computational Linguistics, (October 2013)