YogEx 🌳

যোগ • (jōg) noun

1. connection, link, union
2. addition, sum

                    λ
                   /|\
                  / | \
                 /  |  \
                Y   |   O--------G
               /    |    \      /
              /     |     \    /
             /      |      \  /
            যো------+-------গ
           / \      |      / \
          /   \     |     /   \
         /     \    |    /     \
        ✦       ✦   |   ✦       ✦
                   

Yog is a set of Graph and Network algorithms and data structures implemented in Elixir and packaged as a common API.

There is also a similar library written in Gleam, which I used to learn Gleam by collecting and translating most of the algorithms I have written in Elixir over the years.

Both libraries are actively maintained, with the Elixir version getting new features more frequently, and also sporting more experimental features.

Warning

API Stability: Until the version reaches 0.98.0 1.0.0, there may be breaking changes. While I'll try my best to keep the API stable, there's no guarantee some hiccups in performance, and documentation quality maybe less than optimal. Before version 0.99.0 is released in 12-12-2026, the primary focus is on performance, documentation, and bugfixes. From v0.97.0 onwards, there will be no breaking changes until v2.0 (No plans for that).

Features

YogEx provides comprehensive graph algorithms organized into modules:

Core Capabilities

Pathfinding & Flow — Shortest paths (Dijkstra, A*, Bellman-Ford, Floyd-Warshall, Johnson's), maximum flow (Edmonds-Karp), min-cut (Stoer-Wagner), and implicit state-space search for on-demand graphs.

Network Analysis — Centrality measures (PageRank, betweenness, closeness, eigenvector, Katz), community detection (Louvain, Leiden, Infomap, Walktrap), and network health metrics.

Connectivity & Structure — SCCs (Tarjan/Kosaraju), bridges, articulation points, K-core decomposition, and reachability analysis with exact and HyperLogLog-based estimation.

Graph Operations — Union, intersection, difference, Cartesian product, power, isomorphism, and O(1) transpose.

Developer Experience

Generators & Builders — Classic patterns (complete, cycle, grid, Petersen), random models (SBM, R-MAT), and a comprehensive Maze Generation suite (Recursive Backtracker, Wilson's, Kruskal's, Eller's, etc.) with labeled and grid builders.

I/O & Visualization — GraphML, GDF, Pajek, LEDA, TGF, JSON serialization plus ASCII, DOT, and Mermaid rendering.

Functional (Experimental) — Pure inductive graph library (FGL) for elegant recursive algorithms.

Complete Algorithm Catalog — See all 60+ algorithms, underlying data structures (Pairing Heap, Union-Find, HyperLogLog), and selection guidance with Big-O complexities.

Installation

Basic Installation

Add YogEx to your list of dependencies in mix.exs:

def deps do
  [
    {:yog_ex, "~> 0.98.0"}
  ]
end

Then run:

mix deps.get

Optional Dependencies

YogEx includes several optional dependencies that enable additional I/O and interoperability features:

Dependency	Module	Purpose
:saxy	Yog.IO.GraphML	Fast streaming XML parser for GraphML files (3-4x faster than default :xmerl)
:jason	Yog.IO.JSON	JSON serialization/deserialization for D3.js, Cytoscape, vis.js, NetworkX formats
:libgraph	Yog.IO.Libgraph	Bidirectional conversion with libgraph library

To use these features, add the optional dependencies to your mix.exs:

def deps do
  [
    {:yog_ex, "~> 0.98.0"},
    {:saxy, "~> 1.5"},       # For fast GraphML/XML parsing
    {:jason, "~> 1.4"},      # For JSON import/export
    {:libgraph, "~> 0.16"}   # For libgraph interoperability
  ]
end

XML/GraphML with Saxy

# Reading large GraphML files is significantly faster with saxy
{:ok, graph} = Yog.IO.GraphML.read("large_network.graphml")

# Writing GraphML
Yog.IO.GraphML.write("output.graphml", graph)

JSON Serialization with Jason

# Export to various JSON formats
json = Yog.IO.JSON.to_json(graph, Yog.IO.JSON.export_options_for(:d3_force))

# Import from JSON
{:ok, graph} = Yog.IO.JSON.from_json(json_string)

Libgraph Interoperability

# Convert Yog graph to libgraph
libgraph = Yog.IO.Libgraph.to_libgraph(graph)

# Convert libgraph back to Yog
{:ok, yog_graph} = Yog.IO.Libgraph.from_libgraph(libgraph)

Livebook

For livebook, add the following:

Mix.install(
  {:yog_ex, "~> 0.98.0"}
)

There is a Kino App that can be used to explore the library and create and render graphs.

Usage

alias Yog.Pathfinding

# Create a directed graph
graph =
  Yog.directed()
  |> Yog.add_node(1, "Start")
  |> Yog.add_node(2, "Middle")
  |> Yog.add_node(3, "End")
  |> Yog.add_edge_ensure(from: 1, to: 2, with: 5)
  |> Yog.add_edge_ensure(from: 2, to: 3, with: 3)
  |> Yog.add_edge_ensure(from: 1, to: 3, with: 10)

# Find shortest path using Dijkstra (uses :ok/:error tuples and Path struct)
case Pathfinding.shortest_path(
  in: graph,
  from: 1,
  to: 3
) do
  {:ok, path} ->
    IO.puts("Found path with weight: #{path.weight}")
  :error ->
    IO.puts("No path found")
end
# => Found path with weight: 8

Examples

Detailed examples are located in the examples/ directory

Advent of Code Solutions

YogEx is used to solve Advent of Code challenges.

See all Advent of Code solutions tagged with graph that demonstrate usage of YogEx algorithms in the Advent of Code repository.

Projects Using Yog

Yog powers the following open-source libraries that build domain-specific abstractions on top of its graph engine:

Choreo — Domain-Specific Diagram Builders

Analysis-first diagramming for Elixir. Instead of drawing static pictures, you model systems and get live answers — reachability, cycles, bottlenecks, threat generation, and more.

• Choreo — Infrastructure architecture diagrams (databases, caches, services, queues)
• Choreo.FSM — Finite state machines with determinism checks and shortest accepting paths
• Choreo.Dataflow — Pipeline diagrams with throughput simulation and backpressure detection
• Choreo.Dependency — Software dependency graphs with cycle detection and layer enforcement
• Choreo.DecisionTree — Classification trees with feature importance and pruning
• Choreo.MindMap — Concept mapping with orphan detection and root-to-leaf paths
• Choreo.ThreatModel — STRIDE threat modeling with auto-generated severity scoring
• Choreo.Workflow — Task orchestration with critical-path analysis and Saga-pattern compensations

Tapestry — Graph-Native Domain Engine

Model structured domains as typed multigraphs. Kanban boards, timelines, dependency networks, and structural analysis are all projections of the same underlying graph.

• Project management with milestones, tasks, users, and labels
• Query what blocks a task, what's ready to start, and who's the bottleneck
• Critical-path analysis and transitive dependency tracking
• Renders natively to Mermaid for GitHub, Notion, and Obsidian

Meridian — Spatial Graphs

Projection-aware spatial graphs for Elixir. Brings geography into graph theory with coordinate-reference-system safety, map ingestion, and spatial algorithms.

• Build graphs from H3 hex grids and geohash rectangles
• Ingest and render GeoJSON for road networks and geographic data
• Spatially-informed A*, Dijkstra, and widest-path routing
• CRS-aware edge weights with earth-distance heuristics

Development

Running Tests

mix test

Run tests for a specific module:

mix test test/yog/pathfinding/dijkstra_test.exs

Project Structure

• lib/yog/ — Core graph library modules (pure Elixir)
• test/ — Unit tests and doctests
• examples/ — Real-world usage examples

Property-Based Testing

This library uses property-based testing (PBT) via StreamData to ensure that algorithms hold up against a wide range of automatically generated graph structures.

See the PROPERTIES.md for a complete catalog of all algorithmic invariants (hypotheses) verified by the test suite.

AI Assistance

Parts of this project were developed with the assistance of AI coding tools. All AI-generated code has been reviewed, tested, and validated by the maintainer.