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There are two questions I feel puzzled in the recent period.

  1. Firstly, if given a set of sub-graphs, which are sampled from the underlying graph, how can I infer the underlying graph given the set of observed sub-graphs? If you can refer some good papers to me, I will appreciate it very much. This is just one case.

  2. Another case is that a set of sub-graphs are sampled from several underlying graphs: How can I infer the underlying graphs given the set of observed sub-graphs?

I welcome any comments.

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"Exponential Random Graph Models" - precisely deal with the first case in your question.

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  • $\begingroup$ Thanks very much. I will have a deep look at the paper. Thanks again. Any ideas? $\endgroup$ – Jun Mar 8 '12 at 6:52
  • $\begingroup$ After reading the paper: An introduction to exponential random graph (p^{\star}) models for social network. I find that there exists one assumption that the number of the observed graphs should be the same, for example n. My scenario differs from ERGMs in that the number of the observed graphs is not the same. For example. The underlying graph has 30 nodes. One observed graph has 14 nodes, the other 10, ...Based on the observed graphs, the model that I try to seek is to reconstruct the 30 nodes underlying graphs from those observed graphs with different node numbers. Thanks again.! $\endgroup$ – Jun Mar 8 '12 at 19:48
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    $\begingroup$ Try: B. Olding and P. J. Wolfe. "Inference for graphs and networks: Extending classical tools to modern data." $\endgroup$ – JohnRos Jul 7 '12 at 5:41

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