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I am interested about plotting graphs of a phenomenon and study it using tools from social network analysis.
Suppose the nodes are time series, and that the links between the nodes are the correlation between them. The first issue I have is how to compute the correlation between the nodes. For instance, between two nodes (i.e., between two time series) there may be a lag-0 correlation term, and/or some other lag-n correlation coefficients. Is there a way to get one single number from this? After all, I only want to have one link between two nodes, as multiple links would make the analysis more difficult.

Has any work been done in the literature in this sense, i.e., studying correlation of time series from a social network analysis perspective?

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Can you give an example of the nodes time series? Are these clicks on a social media site? Events of some kind? Where does the input data come from? –  Assad Ebrahim Dec 17 '12 at 23:37
    
a node is a time series. For example, a node may represent the temperature at a particular location, and you want to connect two nodes if there is a correlation between the two time series. The question is how to combine these two time series because, in general, you have correlation at different lags. –  ACAC Dec 17 '12 at 23:48
    
Wouldn't this be a percolation theory problem? Or, rather, isn't this just percolation theory in general? Ah, nevermind, I read your second sentence wrong! –  Arkamis Dec 18 '12 at 19:12
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2 Answers

Some literature is available on Tensor analysis, which might be of relevance in such kind of problems. Search for some papers on- 'Tensor analysis on dynamic graphs'. Introduction to these methods- http://www.graphanalysis.org/SIAM-PP08/Dunlavy.pdf

There have been few recent approaches using Ising model and Gibbs sampling as well to handle such type of data. Some guys from Carnegie are doing work in this directions. Tools/code is open sourced.

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From your description above, you don't need social network analysis per se, but need a network science perspective. I suspect that someone in physics might have used such temperature/time series data and done a network analysis, but you'd have to look at the physics literature. I believe the journal Physica A would deal with this kind of thing, which falls under the umbrella of statistical mechanics.

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