Graph Dynamics Lab

Graph Dynamics Lab is a research-oriented simulation framework for exploring
information propagation, correlation, and entanglement-like dynamics on graphs.

The project is quantum-inspired, but deliberately avoids full quantum formalisms
(Qiskit, density matrices, etc.) in favor of transparent, interpretable models
built from first principles.

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Motivation

Graphs are a universal abstraction:

• physical systems
• data networks
• information flow
• interaction structures

This project treats a graph not as static topology, but as a dynamical system
where:

• nodes carry state amplitudes
• edges define interaction rules
• global behavior emerges from local rules

The goal is understanding dynamics, not maximizing performance.

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Core Concepts

1. Graph as Structure

• adjacency matrix with real or complex weights
• directed or undirected edges
• no external graph libraries (custom implementation)

2. State as Physics

• each node holds a value (real or complex)
• full state is a normalized vector
• normalization enforces physical consistency

3. Evolution as Law

• deterministic linear evolution rule
• graph acts as an operator on the state
• no hidden randomness

4. Time as Simulation

• discrete time steps
• full state history is preserved
• enables post-analysis (entropy, correlation, entanglement)

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Metrics & Analysis

The system is analyzed using information-theoretic and relational measures:

Entropy

• Shannon entropy of node probabilities
• tracks information spreading and l

Future Work

Possible extensions include:

larger and heterogeneous graphs

directed phase-asymmetric dynamics

persistent state logging (CSV / JSON)

C# front-end integration

comparative studies of graph topologies