Core Concepts
Communicability geometry provides insights into analyzing signed graphs in data sciences.
Abstract
The content discusses the concept of communicability geometry for signed graphs, focusing on metrics like communicability distance and angles. It explores applications in data analysis, such as partitioning, dimensionality reduction, and hierarchy detection. Real-world examples include tribal alliances and international relations during wartime.
1. Introduction to Signed Graphs:
- Signed graphs represent data with conflicting interactions.
- Applications in biological, ecological, and social systems.
2. Definitions:
- Defines signed graph components like adjacency matrix and eigenvalues.
- Explains balanced graphs and structural balance theorem.
3. Related Works:
- Discusses distances in signed graphs.
- Covers methods for partitioning and dimensionality reduction.
4. Signed Walks, Factions, and Communicability:
- Explores walks, paths, cycles in signed graphs.
- Introduces balanced graph concepts and switching transformations.
5. Communicability Geometry:
- Defines communicability distance as a Euclidean metric.
- Discusses spherical properties of communicability EDM.
6. Applications - Gahuku-Gama Tribes:
- Analyzes tribal alliances using communicability angle space.
- Hierarchical clustering reveals alliance hierarchy.
7. Applications - International Relations in Wartime:
- Examines WWI international relations using communicability embedding.
- Identifies factions based on network structure changes over time.
Stats
"Signed graphs are an emergent way of representing data."
"Metrics like communicability distance are Euclidean and spherical."
"The study of signed graphs is active in mathematics."
Quotes
"The interactions between entities are extracted from real-world correlations."
"Methods developed can be applied to solve tasks based on similarities between pairs."