Some algorithms ; useful for studying social networks

1. Some random graphs for network models Birgit Plötzeneder

2. Bell-shaped node degree distributions

3. Random model Erdös,Renyi (1960s) On random graphs I; On the evolution of random graphs; On the strength of connectedness of a random grap h - start with N disconnected nodes - connect nodes with probability p to each other

4. Watts and Strogatz Watts, Strogatz (1998), Collective dynamics of "small-world" networks - one-dimensional ring lattice of N nodes connected to its 2 K nearest neighbors - goes through each of the edges in turn and, independently with probability p "rewire" it to a randomly selected (different) node

5. Watts and Strogatz - average distance grows like O(log(N) and not O(N). - support high levels of clustering „ The small-world effect (short average distance between nodes and high levelsof clustering) has been detected in networks that include a network of actors in Hollywood, the power generator network in the western US...“ Gerardo Chowell and Carlos Castillo-Chavez, Worst-Case Scenarios and Epidemics

7. Don't replace edges, instead create shortcuts

8. Power-law degree distributions = Pareto distributions

9. Pareto distributions - small number of highly connected nodes, most nodes have a small number of connections - Barabasi and Albert called them scale-free networks

10. Barabási and Albert Barabàsi, Albert (1999) Emergence of scaling in random networks - starts with a small number of nodes - a new node connects with higher probability to nodes that have already accumulated a higher number of connections

12. Klemm, Eguíluz (2002) Growing scale-free networks with small-world behavior

13. fat-tailed degree distribution

14. Dorogovtsev, Mendes, Samukhin Dorogovtsev, Mendes, Samukhin : How to generate a random growing network - with each step, the edges of a growing network are transformed into configurations of edges and new vertices according to some probability function