In graph theory and network
indicators
of centrality identify
important vertices within a graph. Applications include identifying the most influential
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person(s) in a social network, key infrastructure nodes in the Internet or urban networks,
and super-spreaders of disease. Centrality concepts were first developed in social
network analysis, and many of the terms used to measure
centrality reflect
their sociological origin’
The objective of this programming assignment is to identify the most influential person in
a social network, in order to do we need to apply the Closeness Centrality (CC) algorithm
on a large graph representing a social network.
Definition: Closeness centrality scores each node based on their ‘closeness’ to all other
nodes in the network.
What it tells us: This measure calculates the shortest paths between all nodes, then
assigns each node a score based on its sum of shortest paths. It is calculated as the
average of the shortest path length from the node to every other node in the network.
When to use it: For finding the individuals who are best placed to influence the entire
network most quickly. The more central a node is, the lower its total distance to all other
Thus, the closeness centrality for node D is 0.58.
We do the same process for node A. The table below has all the shortest path lengths.
Here, the average shortest path length is:
Thus, node A’s closeness centrality is 0.29.
As we are using the normalized closeness centrality, higher closeness values mean that
the node is more central, because it means that it takes fewer steps to get to other nodes
So, since D’s value of 0.58 is higher (maximum value is 1) than A’s value of 0.29, D is
more central.
Closeness centrality corresponds the closest to what we see visually. Nodes that are very
central by this measure tend to appear in the middle of a network. A node with strong
closeness centrality also tends to be close to most people. In an investigation, that means
the person will be in a good position to hear from most friends of friends. They will be a
good source of secondhand information since it can reach them quite easily.
Instructions:
You are given a file containing:
The description of the network to be analyzed.(readme.html)
the source code reading this file and extracting the information about the nodes
and their adjacency lists.(Graph.java)
Fill in the starter code ClosenessCentrality.java to identify the 10 most influential
nodes of this network (based on their Closeness Centrality value)
You must submit a short report (suggested max 2 pages) in file report.pdf that
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