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An Information-Theoretic Bound on p-Values for Detecting Communities Shared between Weighted Labeled Graphs.
Predrag Obradovic1, Vladimir Kovačević1, Xiqi Li2
1School of Electrical Engineering, University of Belgrade, 11000 Belgrade, Serbia.
Entropy (Basel, Switzerland)
|July 8, 2023
Summary
This study introduces an enhanced Connect the Dots (CTD) method for efficiently finding highly connected node sets in two networks. The approach establishes information-theoretic bounds, overcoming computational hurdles in network analysis.
Area of Science:
- Network science
- Computational biology
- Social network analysis
Background:
- Community detection is crucial for analyzing complex networks.
- Permutation testing for p-values in network analysis is computationally expensive.
- Existing methods struggle with the high cost of statistical validation.
Purpose of the Study:
- To extend the Connect the Dots (CTD) approach for analyzing pairs of graphs.
- To establish information-theoretic bounds for p-values in community detection.
- To determine lower bounds for the size and connectedness of detectable communities.
Main Methods:
- Extension of the CTD (Connect the Dots) algorithm.
- Application of information-theoretic upper bounds for p-values.
- Analysis of two labeled weighted graphs simultaneously.
Main Results:
- Developed a computationally efficient method for community detection in dual graphs.
- Established information-theoretic upper bounds on p-values, reducing reliance on permutation testing.
- Provided lower bounds for community size and connectedness, enhancing detection capabilities.
Conclusions:
- The extended CTD approach offers a practical solution for analyzing node communities in pairs of networks.
- This method significantly reduces the computational burden associated with statistical significance testing.
- Broadens the applicability of CTD to comparative network analysis.
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