Stacked Linear Algebra Graph

An embedded and in-memory graph using sparse linear algebra.

Capabilities

Architecture

The Stacked Linear Algebra Graph implements a directed graph using GrapBLAS sparse linear algebra. The graph models vertices and adjacency matrices as GraphBLAS sparse vectors and matrices respectively. The graph operates on its vertex vectors and adjacency matrices using GraphBLAS operators.

Data types

The graph stores Rust primitive numeric types in its vertices and edges:

• bool,
• i8
• i16
• i32
• i64
• u8
• u16
• u32
• u64
• f32,
• f64,
• isize
• usize

Indexing

The graph has a dual indexing system - string keys for human understandability and numerical indices for efficiency. Each coordinate maps to both a user-defined unique string key and an unsigned integer index assigned by the graph. Integer indices may be reused by the graph after its key was deleted.

Upon creating a new vertex type, the graph creates a vertex vector for each supported primitive numeric type. Equivalently, upon creating a new edge type the graph creates a new adjacency matrix for each supported value type.

The numerical vertex indices, and their associated keys, reference the same coordinates in all vertex vectors and adjacency matrices. All vertex vectors and adjacency matrices thus have compatible sizes.

Each combination of vertex vector and adjacency matrix thus defines a separate graph. All graphs share the same coordinates.

Linear algebra operations

Graph operators apply to any applicable combination of vertex vector and adjacency matrix.

ACID

Cairn Knowledge Graph does currently not guarantee ACID database transaction properties.

Persistence

The graph resides in-memory and does currently not exist in persistent storage.

Minimum example

use graphblas_sparse_linear_algebra::operators::binary_operator::{
        Assignment, Plus,
    };
    use graphblas_sparse_linear_algebra::operators::index_unary_operator::IsValueEqualTo;
    
    use graphblas_sparse_linear_algebra::operators::options::OperatorOptions;
    use graphblas_sparse_linear_algebra::operators::semiring::PlusTimes;

    use stacked_linear_algebra_graph::graph::edge::{
        DirectedEdgeCoordinateDefinedByIndices,
        WeightedDirectedEdgeDefinedByIndices,
    };
    
    use stacked_linear_algebra_graph::graph::graph::Graph;
    use stacked_linear_algebra_graph::graph::vertex::VertexDefinedByKey;
    use stacked_linear_algebra_graph::operators::add::{
        AddEdge, AddEdgeType, AddVertexType, AddVertex
    };
    use stacked_linear_algebra_graph::operators::apply_operator::ApplyIndexUnaryOperatorToVertexVector;
    use stacked_linear_algebra_graph::operators::element_wise_multiplication
        ::BinaryOperatorElementWiseVertexVectorMultiplication;
    use stacked_linear_algebra_graph::operators::multiplication
        ::VertexVectorAdjacencyMatrixMultiplication;
    use stacked_linear_algebra_graph::operators::read::ReadVertexValue;

    fn main() {
        let mut graph = Graph::with_initial_capacity(&5, &5, &5).unwrap();

        let numbers_vertex_type_key = "numbers";
        let odd_number_sequence_edge_type_key = "odd_number_sequence";

        let _vertex_type_1_index = graph.add_new_vertex_type(numbers_vertex_type_key).unwrap();

        // Add vertices
        let mut vertex_indices = Vec::new();
        for n in 0..12 {
            vertex_indices.push(
                graph
                    .add_new_vertex(VertexDefinedByKey::new(
                        numbers_vertex_type_key,
                        format!("vertex_{}", n).as_str(),
                        &(n as u8),
                    ))
                    .unwrap(),
            );
        }

        let odd_number_sequence_edge_type_index = graph
            .add_new_edge_type(odd_number_sequence_edge_type_key)
            .unwrap();

        // Define a sequence of subsequent odd numbers
        for i in [1, 3, 5, 7, 9] {
            let edge = WeightedDirectedEdgeDefinedByIndices::new(
                DirectedEdgeCoordinateDefinedByIndices::new(
                    odd_number_sequence_edge_type_index,
                    vertex_indices[i],
                    vertex_indices[i + 2],
                ),
                true,
            );

            graph.add_new_edge_using_indices(edge).unwrap();
        }

        // Find the fourth number in the sequence, starting at 1
        let selected_vertices_key = "selected_vertices";
        let selected_vertices_index = graph.add_new_vertex_type(selected_vertices_key).unwrap();

        ApplyIndexUnaryOperatorToVertexVector::<u8, u8, u8>::with_key(
            &mut graph,
            numbers_vertex_type_key,
            &IsValueEqualTo::<u8>::new(),
            &1,
            &Assignment::new(),
            selected_vertices_key,
            &OperatorOptions::new_default(),
        )
        .unwrap();

        for _i in 0..2 {
            VertexVectorAdjacencyMatrixMultiplication::<u8, bool, u8, u8>::by_index(
                &mut graph,
                &selected_vertices_index,
                &PlusTimes::<u8>::new(),
                &odd_number_sequence_edge_type_index,
                &Assignment::new(),
                &selected_vertices_index,
                &OperatorOptions::new_default(),
            )
            .unwrap();
        }

        BinaryOperatorElementWiseVertexVectorMultiplication::<u8, u8, u8, u8>::by_key(
            &mut graph,
            selected_vertices_key,
            &Plus::<u8>::new(),
            numbers_vertex_type_key,
            &Assignment::new(),
            selected_vertices_key,
            &OperatorOptions::new_default(),
        )
        .unwrap();

        assert_eq!(
            ReadVertexValue::<u8>::vertex_value_by_key(&graph, selected_vertices_key, "vertex_7")
                .unwrap(),
            Some(7)
        )
    }

Requirements

Please make sure to meet the requirements for building graphblas_sparse_linear_algebra.

Contributing

Awesome, contributions are welcome. stacked_linear_algebra_graph and your contribution may be relicensed and integrated into commercial software in the future. Therefore, you will be asked to agree to the Contributor License Agreement when you make a pull request.

Licensing

stacked_linear_algebra_graph is licensed under Creative Commons Attribution Non Commercial 4.0 International. For other licensing options, please contact Sam Dekker.

Acknowledgements

Stacked Linear Algebra Graph is inspired by LAGraph and uses the same underlying GraphBLAS implementation from Timothy A. Davis.