Yog.IO.Matrix (YogEx v0.70.0)

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Adjacency matrix import/export for graph serialization.

This module provides functions to convert between Yog.Graph structures and adjacency matrix representations. Adjacency matrices are commonly used in graph databases (like House of Graphs), mathematical graph theory, and dense graph representations.

Format

An adjacency matrix is a square matrix where matrix[i][j] represents the weight of the edge from node i to node j. A value of 0 or nil indicates no edge.

Example

# Unweighted graph matrix (1 = edge exists, 0 = no edge)
matrix = [
  [0, 1, 1, 0],
  [1, 0, 0, 1],
  [1, 0, 0, 1],
  [0, 1, 1, 0]
]

graph = Yog.IO.Matrix.from_matrix(:undirected, matrix)

Use Cases

  • Importing graphs from House of Graphs database
  • Working with mathematical graph definitions
  • Dense graph representations
  • Interoperability with matrix-based graph libraries

See Also

Summary

Functions

from_matrix(type, matrix)

Creates a graph from an adjacency matrix.

to_matrix(graph)

Exports a graph to an adjacency matrix representation.

Functions

from_matrix(type, matrix)

@spec from_matrix(:directed | :undirected, [[number()]]) :: Yog.graph()

Creates a graph from an adjacency matrix.

The adjacency matrix is a square matrix where matrix[i][j] represents the weight of the edge from node i to node j. A value of 0 or nil indicates no edge.

Parameters

  • type - :directed or :undirected
  • matrix - Square matrix (list of lists) representing edge weights

Examples

iex> # Unweighted adjacency matrix (1 = edge exists)
...> matrix = [
...>   [0, 1, 1, 0],
...>   [1, 0, 0, 1],
...>   [1, 0, 0, 1],
...>   [0, 1, 1, 0]
...> ]
iex> graph = Yog.IO.Matrix.from_matrix(:undirected, matrix)
iex> Yog.Model.order(graph)
4
iex> Yog.Model.edge_count(graph)
4

iex> # Weighted adjacency matrix
...> weighted = [
...>   [0, 5, 3, 0],
...>   [0, 0, 0, 2],
...>   [0, 0, 0, 7],
...>   [0, 0, 0, 0]
...> ]
iex> digraph = Yog.IO.Matrix.from_matrix(:directed, weighted)
iex> Yog.Model.edge_count(digraph)
4

Notes

  • Node IDs are assigned as integers 0, 1, 2, ... based on matrix row indices
  • For undirected graphs, only the upper triangle is processed (i < j) to avoid duplicate edges
  • Zero values and nil are treated as "no edge"

Raises

to_matrix(graph)

@spec to_matrix(Yog.graph()) :: {[Yog.node_id()], [[number()]]}

Exports a graph to an adjacency matrix representation.

Returns a tuple {nodes, matrix} where:

  • nodes is a list of node IDs in the order they appear in the matrix
  • matrix is the adjacency matrix (list of lists)

Examples

iex> graph = Yog.undirected()
...>   |> Yog.add_node(1, nil)
...>   |> Yog.add_node(2, nil)
...>   |> Yog.add_node(3, nil)
...>   |> Yog.add_edge!(from: 1, to: 2, with: 5)
...>   |> Yog.add_edge!(from: 2, to: 3, with: 7)
iex> {nodes, matrix} = Yog.IO.Matrix.to_matrix(graph)
iex> nodes
[1, 2, 3]
iex> matrix
[[0, 5, 0], [5, 0, 7], [0, 7, 0]]

Notes

  • Unconnected node pairs have weight 0 in the matrix
  • For undirected graphs, the matrix is symmetric
  • Node order is deterministic (sorted by node ID)