# Networks. Graphs (undirected, unweighted) has a set of vertices V has a set of undirected, unweighted edges E graph G = (V, E), where.

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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 e ij 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 v i, take every edge v i, v j (i < j) and rewire it with probability p. -Rewiring is done by replacing e ij with e ik 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 v i. -Connect v i to v j according to the preferential attachment rule: k i … 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 = 1 C = 2/3 C = 1/3 C = 0 -average Clustering coefficient -Topological coefficient -Average topological coefficient of vertex i if i and j interact otherwise 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

Cytoscape http://www.cytoscape.org.sif files: contain the network as edge list (i.e. ).NA files: contain attributes of nodes (i.e. = ).EA files: contain attributes of edges (i.e. (identifier) = )

http://learnxinyminutes.com/docs/python/ Python http://networkx.github.io

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