Mendz.Graphs Sparse Matrices

Mendz.Graphs provides a set of concrete sparse matrix implementations. Compared to dense matrices, sparse matrices save on memory by using only what's needed to represent the graph.

Summing up, Mendz.Graphs provides the following sparse matrix classes/types:

• AdjacencyMatrixBase is the base class of sparse adjacency matrices.
• AdjacencyMatrix represents a sparse (1, 0, 0)-adjacency list.
• WeightedAdjacencyMatrix represents a sparse weighted adjacency matrix.
• SeidelAdjacencyMatrix represents a sparse (-1, 1, 0)-adjacency matrix.
• LaplacianMatrix represents a sparse (-1, 0, d)-adjacency matrix, where d is the degree of the vertex.
• GenericAdjacencyMatrix provides a generic sparse (a, b, c)-adjacency matrix implementation.
• DegreeMatrix, InDegreeMatrix and OutDegreeMatrix represent sparse diagonal matrices of vertex degrees.
• IncidenceMatrix represents a sparse incidence matrix.

Remember that Mendz.Graphs is not a intended to be a Math library. Mendz.Graphs is all about graph data and representing them. Thus, the focus of Mendz.Graphs.Representations.Matrices is how that "rectangular array" mentioned in the matrix definition can be created, initialized and filled with graph data. The matrices that you create using Mendz.Graphs can be passed to Math libraries that support operations with matrices. There are many .Net compatible Math/numerical libraries available like Math.NET, ALGLIB and MATLAB. See also this list from Wikipedia. A quick search works to find them, too!

Mendz.Graphs intentionally does not include algorithms. I encourage developers to build their own algorithm library or libraries based on Mendz.Graphs.