# Graph-Tensor Integration Implementation

## Overview

This document describes the Graph-Tensor deep integration implemented for God-Graph v0.4.0-tensor-alpha. The integration enables seamless conversion between graph structures and tensor representations, which is essential for Graph Neural Network (GNN) workflows.

## Implementation Details

### New Module: `src/tensor/graph_tensor.rs`

The new `graph_tensor` module provides comprehensive graph-tensor conversion capabilities:

#### Core Types

1. **`GraphAdjacencyMatrix`**
   - Sparse adjacency matrix representation in CSR format
   - Methods:
     - `from_edge_list()`: Create from edge list
     - `to_coo()`: Convert to COO format
     - `normalized_with_self_loops()`: Compute D^(-1/2) * (A + I) * D^(-1/2) for GCN
     - `degree_matrix()`: Extract degree matrix
     - `inverse_degree_matrix()`: Compute inverse degrees for normalization

2. **`GraphFeatureExtractor<'a, T, E>`**
   - Extract tensor representations from graphs
   - Methods:
     - `extract_node_features_scalar()`: Extract scalar node features
     - `extract_node_features()`: Extract multi-dimensional node features
     - `extract_edge_features()`: Extract edge features
     - `extract_adjacency()`: Extract adjacency matrix
     - `extract_all()`: Complete graph-to-tensor conversion

3. **`GraphReconstructor`**
   - Reconstruct graphs from tensor representations
   - Methods:
     - `from_adjacency()`: Reconstruct from adjacency matrix
     - `from_coo()`: Reconstruct from COO tensor

4. **`GraphTensorExt<T, E>` (Extension Trait)**
   - Adds tensor conversion methods to `Graph` type
   - Methods:
     - `to_tensor_representation()`: Convert graph to (features, adjacency) tuple
     - `adjacency_matrix()`: Get adjacency matrix
     - `node_features()`: Extract node features
     - `feature_extractor()`: Create feature extractor

5. **`GraphBatch`**
   - Batch multiple graphs for efficient processing
   - Methods:
     - `new()`: Create batch from graphs
     - `batch_features()`: Get concatenated feature matrix
     - `batch_adjacency()`: Get block-diagonal adjacency matrix

## Usage Examples

### Basic Graph to Tensor Conversion

```rust
use god_gragh::graph::Graph;
use god_gragh::tensor::GraphTensorExt;

// Create a graph with vector node features
let mut graph = Graph::<Vec<f64>, f64>::directed();

let n0 = graph.add_node(vec![1.0, 0.0]).unwrap();
let n1 = graph.add_node(vec![0.0, 1.0]).unwrap();
let n2 = graph.add_node(vec![1.0, 1.0]).unwrap();

let _ = graph.add_edge(n0, n1, 1.0);
let _ = graph.add_edge(n1, n2, 1.0);
let _ = graph.add_edge(n2, n0, 1.0);

// Convert to tensor representation
let (features, adjacency) = graph.to_tensor_representation().unwrap();

assert_eq!(features.shape(), &[3, 2]);
assert_eq!(adjacency.num_nodes, 3);
```

### Custom Feature Extraction

```rust
use god_gragh::graph::Graph;
use god_gragh::tensor::GraphFeatureExtractor;

let mut graph = Graph::<String, f64>::directed();
let n0 = graph.add_node("node0".to_string()).unwrap();
let n1 = graph.add_node("node1".to_string()).unwrap();
let _ = graph.add_edge(n0, n1, 1.0);

let extractor = graph.feature_extractor();

// Extract scalar features (string length)
let features = extractor.extract_node_features_scalar(|s| s.len() as f64).unwrap();
assert_eq!(features.shape(), &[2, 1]);
```

### Graph Reconstruction

```rust
use god_gragh::graph::Graph;
use god_gragh::tensor::{GraphAdjacencyMatrix, GraphReconstructor};

// Create adjacency matrix from edge list
let edges = vec![(0, 1), (1, 2), (2, 0)];
let adj = GraphAdjacencyMatrix::from_edge_list(&edges, 3, true).unwrap();

// Reconstruct graph
let reconstructor = GraphReconstructor::new(true);
let graph: Graph<usize, f64> = reconstructor
    .from_adjacency(
        &adj,
        |i| i,              // Node factory
        |_src, _dst, w| w,  // Edge factory
    )
    .unwrap();

assert_eq!(graph.node_count(), 3);
assert_eq!(graph.edge_count(), 3);
```

### Batch Processing

```rust
use god_gragh::graph::Graph;
use god_gragh::tensor::GraphBatch;

// Create multiple graphs
let mut graph1 = Graph::<Vec<f64>, f64>::directed();
let n0 = graph1.add_node(vec![1.0, 0.0]).unwrap();
let n1 = graph1.add_node(vec![0.0, 1.0]).unwrap();
let _ = graph1.add_edge(n0, n1, 1.0);

let mut graph2 = Graph::<Vec<f64>, f64>::directed();
let n0 = graph2.add_node(vec![1.0, 1.0]).unwrap();
let n1 = graph2.add_node(vec![0.0, 0.0]).unwrap();
let _ = graph2.add_edge(n0, n1, 1.0);

// Create batch
let batch = GraphBatch::new(&[graph1, graph2]).unwrap();

let batch_features = batch.batch_features();
let batch_adjacency = batch.batch_adjacency();

assert_eq!(batch.len(), 2);
```

## GNN Integration

The graph-tensor integration is designed to work seamlessly with the existing GNN primitives:

```rust
use god_gragh::graph::Graph;
use god_gragh::tensor::{GraphTensorExt, GCNConv, MessagePassingLayer};

// Prepare graph data
let mut graph = Graph::<Vec<f64>, f64>::directed();
// ... add nodes and edges ...

let (features, adjacency) = graph.to_tensor_representation().unwrap();

// Compute normalized adjacency for GCN
let normalized_adj = adjacency.normalized_with_self_loops().unwrap();

// Apply GCN convolution
let gcn = GCNConv::new(in_features, out_features);
let output = gcn.forward(&features, &normalized_adj);
```

## Performance Characteristics

- **Memory Efficiency**: Uses sparse CSR format for adjacency matrices
- **Zero-Copy Views**: `GraphFeatureExtractor` borrows from original graph
- **Batch Processing**: `GraphBatch` enables efficient mini-batch GNN training
- **Format Conversion**: COO/CSR conversion optimized for different operations

## Testing

All functionality is covered by comprehensive unit tests:

```bash
cargo test --features "tensor,tensor-sparse,tensor-gnn,tensor-pool" --lib tensor::graph_tensor
```

Test coverage includes:
- Adjacency matrix creation and conversion
- Feature extraction (scalar and multi-dimensional)
- Graph reconstruction from tensors
- Normalized adjacency computation
- Batch processing

## Future Enhancements

1. **Automatic Differentiation**: Integration with autograd engine for backpropagation
2. **GPU Acceleration**: Direct tensor operations on GPU via Dfdx/Candle backends
3. **Advanced Sampling**: Neighbor sampling for large-scale GNN training
4. **Heterogeneous Graphs**: Support for multiple node/edge types
5. **Dynamic Graphs**: Time-varying graph tensor representations

## Version Information

- **Target Version**: v0.4.0-tensor-alpha
- **Feature Flags**: `tensor`, `tensor-sparse`, `tensor-gnn`, `tensor-pool`
- **Rust Version**: 1.85+
- **License**: MIT OR Apache-2.0

## See Also

- `TENSOR_OPTIMIZATION_REPORT.md`: Comprehensive tensor optimization plan
- `src/tensor/gnn.rs`: GNN primitives implementation
- `src/tensor/backend.rs`: Multi-backend abstraction layer
- `src/tensor/pool.rs`: Memory pool optimization
