How can we compare the evolution of two networks?
For example, if we want to compare the evolution of facebook with twitter, what measures which would help us to get the insight of evolution processes of these two networks?
For instance, if we take facebook and twiiter network's snapshots with the time interval of 3 months or 6 months (over the period of several years) and then would we see how the vertex, edges, or even global properties like clustering coefficient, modularity etc. are varying over the time?
Then how could we conclude that they are evolving with the same rate, style, way, type or if there is a significant difference between the evolution process of these networks?
Dear Dr Gupta.
Your question is about what to measure and more specifically about to measure it. Indeed, can it be measured? You clearly recognise that such an enquiry involves multiple inspections of networks: you mention 3-monthly snapshots.
Over that time period new users will join the application, be it Facebook or Twitter. Additionally, some will cancel their accounts. So what seems like a simple, single measure is now two: new accounts and cancellations. Is the rate of new accounts greater, equal or less than rate of cancellations? These seem to me to be important figures.
Secondly, some personal networks will change: some will expand, others stay the same, and others may contract. So again we need to look at three counts here. Again these different rates appear to be important and need consideration in your method.
Perhaps the most interesting aspect will be to inspect how personal networks have added ties that connect an ego to other networks through perhaps a weak tie. Regardless of the strength (and how do you measure the strength of ties on Face book: by number of transactions, the emotional strength of the transaction .. I don’t know) of the tie, an examination of how a sampled number of account holder’s networks have changed (grown?) over time may be something that you can measure.
All of the above is about ego networks and there are some simple measures we can use with such networks (see Scott (2000) for the theory and Cross and Parker (2004) for some excellent examples).
After thinking about your question for 20 minutes or so, it does seem that sampling the millions of Facebook users and Twitters account holders may be a way in.
You might like to contact Dr Bernie Hogan at Oxford. His current research is looking at internet networks. He may be contacted on [email protected].
Regards ..
Roy Greenhalgh
Cross, R. and A. Parker (2004). The hidden power of social networks. Boston, Mass., Harvard Business School Press.
Scott, J. (2000). Social network analysis: a handbook. London, Sage Publications Ltd.
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