Networks

Graphs(undirected, unweighted)

• has a set of vertices V• has a set of undirected, unweighted edges E• graph G = (V, E), where

Network models-Random graph (Erdoes-Renyi)

algorithm:- number of vertices |V| is constant.- run through all pairs of vertices ij (i < j) and establish an edge eij

with probability p.

Network models-Small world (Watts-Strogatz)

algorithm:- number of vertices |V| is constant.- Construct a regular ring lattice (i.e. a graph with nodes each connected to K, K/2 neighbors on each side.- For every node vi, take every edge vi, vj (i < j) and rewire it with probability p.- Rewiring is done by replacing eij with eik where k is chosen randomly.

Network models-Preferential attachment (Barabasi-Albert)

algorithm:- number of vertices |V| is growing.- In every step, add a new node vi. - Connect vi to vj according to the preferential attachment rule:

ki … degree (i.e. number of neighbors) of vertex i

Network measures- node degree distribution (i.e. histogram of the number of neighbors of each node i)

- clustering coefficient of node i

C = 1C = 2/3C = 1/3C = 0

- average Clustering coefficient

- Topological coefficient

- Average topological coefficient of vertex i

if i and j interactotherwise

neighbors if vertex i

Network measures (contd.)

- average shortest path, diameter

- Betweeness centrality of vertex i

- Neighborhood connectivity of vertex i

- Closeness centrality of vertex i

Cytoscapehttp://www.cytoscape.org

.sif files: contain the network as edge list (i.e. <node 1> <identifier> <node 2>)

.NA files: contain attributes of nodes (i.e. <node> = <attribute>)

.EA files: contain attributes of edges (i.e. <node 1> (identifier) <node 2> = <attribute>)

http://learnxinyminutes.com/docs/python/

Python

http://networkx.github.io