Deep graphs-A general framework to represent and analyze heterogeneous complex systems across scales.

Area of Science:

• Network theory
• Data analysis
• Complex systems

Background:

• Traditional network theory struggles with complex systems' heterogeneity and scale.
• Existing representations lack explicit association of information with diverse objects and relations.
• Need for a unified framework to represent multi-scale properties and interactions.

Purpose of the Study:

• To introduce a generalized network framework, 'deep graphs', unifying existing representations.
• To extend network theory by incorporating heterogeneous properties and multi-scale interactions.
• To provide a scalable data analysis toolkit for complex systems.

Main Methods:

• Defining nodes and edges as sets of arbitrary properties.
• Applying partition lattices to create supernodes and superedges for information aggregation.
• Developing a 'deep graph' representation derived from partition lattices.
• Deriving multilayer network representations from the deep graph framework.

Main Results:

• A unified and generalized network representation ('deep graphs') is established.
• The framework enables analysis of heterogeneous properties and interactions across all scales.
• A scalable software package integrating with the PyData ecosystem is provided.
• Demonstrated application to 16 years of global precipitation data for spat-temporal cluster analysis.

Conclusions:

• Deep graphs offer a comprehensive and scalable solution for complex network data analysis.
• The framework unifies and extends existing network theories, enabling richer insights.
• Applications in analyzing real-world data, such as climate patterns, are feasible and beneficial.