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Friday, June 21, 2013

On Centrality and Power in social networks

After the last weeks post on 'Trust' - - let us quickly review another important measure of (social) network structure.

Centrality is a structural measure of a network that gives an indication of relative importance of a node in the graph / network.
Simplest way of measuring centrality is by counting the number of connections a node has. This is called 'degree centrality'.

Another way of measuring centrality is to see how far a node from all other nodes of the graph is is. This measure is called as 'closeness centrality' as it measures the path length between pairs of nodes.

'Betweenness Centrality' is the measure of number of times the node acting as a bridge on the shortest path of any other two nodes. That gives how important each n ode in connecting the whole network.

To complicate the centrality further, we have a measure called 'eigenvector centrality'. Eigenvector considers the influence for the node in the network. This methods considers the power of the nodes the current node is connected. To explain it simply, if I am connected to 500 other people on LinkedIn is different from Barak Obama connecting to 500 of his friends on the LinkedIn. His 500 connections are more influential (probably) than my 500 connections. Google's page rank is a variant of Eigenvector Centrality.

When an external factor is considered for each node and implement eigenvector centrality to consider an external α it is called 'alpha centrality'

When we move the alpha centrality measure from one node to cover multiple radii to include first degree, second degree and so on.. With a factors of β(i) and measure the centrality as a function of influence of varying degrees, it is called beta centrality.

The key problem with centrality computation is the amount of computing power needed to arrive at the beta centrality measure of the social network with millions of nodes. I recently came across this paper - which proposes an alternative approximation algorithm which is computationally efficient to estimate fairly accurate centrality measure. This alter-based non recursive method works well on non-bipartite networks and suits well for social networks.

Title of this blog states "power" and whole content did not mention anything about it. Generally centrality is considered as the indicator of power or influence. But in some situations power is not directly proportional to centrality. Think about it.
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