To understand and predict behaviors of complex networks and the processes that run on them, one has to be able to do statistical analysis of networks. This requires a mathematical framework that allows for the construction of network ensembles that mimic the structural properties of the complex network but are completely unbiased to everything else. In addition, we need proper statistical estimators to infer structural properties of real-world networks.
I am developing a mathematical framework for statistical analysis of networks using the concept of maximum entropy from Information Theory together with notions from dense graph limits and recent work on sparse graph limits and exchangeable random graphs.
The main research objectives are:
- Design a general framework for generating and analyzing sparse maximum entropy graphs.
- Analyze structure of maximum entropy sparse graphs with given degrees and triangles
- Characterize bias in maximum entropy graphs of finite size
- Develop efficient algorithms to generate and analyze maximum entropy graphs
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