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Volume 16 — Collapse Graphs and Structure Networks

Network Theory in Golden-Base Space​

This volume applies graph theory to collapse structures. Trace networks form complex graphs where nodes are trace states and edges are valid transformations, all respecting the φ-constraint.

Chapter Index​

Chapter 256: NodeGraph​

Collapse Trace Networks as Structural Graphs

Basic graph representation of traces.

Chapter 257: TraceDepGraph​

Graphs of Tensor Trace Dependencies

Dependency analysis in trace networks.

Chapter 258: CollapseCluster​

Clustering Collapse Paths by φ-Topology

Graph clustering algorithms.

Chapter 259: AdjacencyTensor​

StructureNode Adjacency and Collapse Compatibility

Tensor representations of graphs.

Links Across Threads in Collapse Trace Systems

Multi-threaded trace connections.

Chapter 261: GraphEntropy​

Entropic Complexity Metrics for Collapse Graphs

Information content of graph structures.

Chapter 262: CycleDetect​

Detecting Structural Cycles in Collapse Networks

Cycle analysis in trace graphs.

Chapter 263: RewriteGraph​

Collapse Rewrite Rules Applied to Structure Graphs

Graph transformation systems.

Chapter 264: ObsProjGraph​

Observer-Centric Projections of Structural Graphs

Observer views of networks.

Chapter 265: CollapseZone​

Influence Zones in Collapse Trace Graphs

Locality and influence regions.

Chapter 266: IsoTrace​

Graph-Theoretic Tests for Trace Structure Isomorphism

Isomorphism detection algorithms.

Chapter 267: CentralityCollapse​

Centrality Metrics for Structure Nodes

Important nodes in trace networks.

Chapter 268: EntangleGraph​

Tensor Entanglement Graph Representations

Quantum-like entanglement in graphs.

Chapter 269: TraceHeatmap​

Collapse Frequency Heatmaps on Trace Networks

Visualization of activity patterns.

Chapter 270: CollapsePropagate​

Dynamic Collapse Propagation Through Trace Graphs

Information flow dynamics.

Chapter 271: CodexGraph​

Full Codex StructureNode Network as Executable Graph

The codex itself as a graph.

Key Concepts Introduced​

  1. Trace Graphs: Network representations
  2. Graph Clustering: Topological grouping
  3. Cycle Detection: Loop structures
  4. Graph Transforms: Rewrite systems
  5. Centrality: Node importance
  6. Dynamic Propagation: Information flow

Dependencies​

  • Volume 4: Topology foundations
  • Volume 8: Information metrics
  • Volume 14: Module networks

Next Steps​

  • Volume 26: Graph visualization tools
  • Volume 29: Graph rewriting
  • Volume 31: Reality networks

"Networks weave the golden web of connection."