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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.

Friday, June 14, 2013

Trust modeling in social media


After last week’s “tie strength” post, this week let me give some fundamentals on importance of modeling TRUST in social media.

What is Trust?
It is difficult to define. But when I ask “Will you loan a moderate amount to the other person?” or “Will you seek a reference or recommendation regarding a key decision?” help understand the term TRUST.

There are two components to TRUST. Some people are more trusting than others. Some quickly establish trust where as others take a long time in establishing the trust. This component is not easy to be modeled. The second component is the credibility of the trusted person.

Measuring Trust:
In social media, the second component can be measured by analyzing the sentiment based on the blogs referenced by others. This is called “network based trust inference”.

This paper describes a model for measuring trust using link polarity.

Have a good weekend reading!

Friday, June 7, 2013

"tie strength" in social media

What is "tie strength”?

When analyzing the social web, we see various edges (ties or relationships) connecting the nodes (individuals or organizations). Theoretically the strength of the edge or relationship is categorized as strong or weak. In 1973 paper titled "The strength of weak ties" -  Mark Granovetter lays foundations of importance of strength of ties in micro and macro levels of sociology.

Predictive model
Recently I came across a predictive model developed using Facebook which considers seven dimensions of "tie strength" They are: Intensity, Intimacy, Duration, Reciprocal Services, Structural, Emotional Support and Social Distance.

32 Predictive variables from Facebook interactions have been used along with a survey deriving 5 dependent variables that fits into the predictive model.
The model uses statistical linier method to predict the strength of a relationship in continuous 0 - 1 Scale.

More on -

I like the methodology used and practical approach towards predictive modelling. More stronger the tie, better influence....