Characterizing the Complexity of Weighted Networks via Graph Embedding and Point Pattern Analysis.

Area of Science:

• Network Science
• Computational Neuroscience
• Data Science

Background:

• Weighted complex networks model intricate systems like financial markets and brain connectivity.
• Existing entropy methods are limited for assessing complexity in large, weighted networks.
• Quantifying non-randomness and complexity in weighted networks remains a significant challenge.

Purpose of the Study:

• To introduce a novel analytical framework for measuring the complexity of weighted complex networks.
• To address the unmet need for robust complexity metrics in large-scale weighted network analysis.
• To apply the developed method to investigate brain connectivity differences in schizophrenia.

Main Methods:

• Utilizing graph embedding to project network nodes into a low-dimensional vector space.
• Applying point pattern analysis to assess the distribution of projected nodes.
• Measuring deviation from complete spatial randomness to quantify network complexity.

Main Results:

• The proposed method effectively detects complexity differences and demonstrates robustness against noise in simulations.
• Functional brain connectivity networks in male schizophrenic patients exhibit altered complexity compared to healthy controls.
• Sex-specific differences in brain network organization were observed, aligning with known schizophrenia patterns.

Conclusions:

• The new graph embedding and point pattern analysis framework provides a sensitive measure for weighted network complexity.
• The findings highlight potential sex-specific alterations in brain circuitry organization in schizophrenia.
• This method offers a valuable tool for analyzing complex systems across various scientific domains.