Direction Matters: On Influence-Preserving Graph Summarization and Max-Cut Principle for Directed Graphs

Area of Science:

• Graph theory
• Network analysis
• Data summarization

Background:

• Summarizing large-scale directed graphs is challenging.
• Conventional clustering methods lose directed edge information.
• Preserving directed edges is key for graph representation learning.

Purpose of the Study:

• Develop a model for summarizing directed graphs while preserving edge information.
• Utilize reconstruction error minimization with non-negative constraints.
• Relate the model to a Max-Cut criterion for node and relation identification.

Main Methods:

• Proposed a model minimizing reconstruction error with non-negative constraints.
• Developed a multiplicative update algorithm with column-wise normalization.
• Provided theoretical analysis on model identifiability and algorithm convergence.

Main Results:

• The proposed method accurately summarizes directed graphs.
• The summarized graphs are easier to analyze and extract group-level features.
• Experimental results demonstrate the accuracy and robustness of the method.

Conclusions:

• The novel method effectively compresses directed graphs while retaining essential information.
• This facilitates easier analysis and identification of group behaviors for interventions.
• The model and algorithm offer a robust solution for directed graph summarization.