Description
This programming assignment is about computing the centrality properties of the nodes of a ProteinProtein 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 closenesscentrality of node u is defined as the reciprocal of this sum:
where d u,v is the length of a shortest path between u and v.
The Eccentricity of a node is defined as:
E(u)=maxvevd(u,v)
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 ProteinProtein Interaction (PPI) graph of the herpes Kaposi virus. The file kshv is available on canvas.
Output:

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

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.

Using cytoscape, display:

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

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