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Project 5 –  Centrality of nodes in networks

Project 5 –  Centrality of nodes in networks

This programming assignment is about computing the centrality properties of the nodes of a Protein-Protein Interaction (PPI) network. Recall that a PPI network is represented by a graph G=(V,E) where nodes of V represent proteins and an edge of E connecting two nodes represents interacting proteins (either physically or functionally).

You will compute two properties: Closeness centrality and Eccentricity

A detailed description of closeness centrality and eccentricity follows.

The Closeness centrality of a node is a measure of centrality that uses information about the length of the shortest paths within a network; it uses the sum of the shortest distances of a node to all other nodes. Precisely, the closeness-centrality of node u is defined as the reciprocal of this sum:     



where is the length of a shortest path between u and v.

The Eccentricity of a node is defined as:



Define the center of a graph as the node with minimum eccentricity.

Your program computes for each node its closeness centrality and eccentricity value.

Input:  the Protein-Protein Interaction (PPI) graph of the herpes Kaposi virus. The file kshv is available on canvas.

Output:

1.      Print the top 3 nodes (sorted) with the highest closeness centrality value and for each of them print its closeness centrality value.

2.      Print a shortest path between the two nodes with highest and lowest closeness centrality. For that,  you need to have reconstructed the shortest path between the two nodes.

3.      Using cytoscape, display:

a.      the top 3 nodes (sorted) with the highest closeness centrality

b.      the center of the graph, i.e. the node with highest  eccentricity value. Color the center with a different color.

Electronically submit 1). ipython notebook. 2) screen shot of cytoscape display

 

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