# YogEx v0.70.0 - Table of Contents

A comprehensive pure Elixir graph algorithm library

## Pages

- [YogEx 🌳](readme.md)
- [Changelog](changelog.md)

## Modules

- [Yog](Yog.md): Yog - A comprehensive graph algorithm library for Elixir.
- [Yog.Builder.Grid](Yog.Builder.Grid.md): Convenience builder for 2D Grid graphs from nested lists.
- [Yog.Builder.GridGraph](Yog.Builder.GridGraph.md): Grid graph builder result.
- [Yog.Builder.Labeled](Yog.Builder.Labeled.md): Build graphs using arbitrary labels instead of integer IDs.
- [Yog.Builder.Live](Yog.Builder.Live.md): A live builder for incremental graph construction with label-to-ID registry.
- [Yog.Builder.Toroidal](Yog.Builder.Toroidal.md): Toroidal grid builder - grids where edges wrap around.
- [Yog.Builder.ToroidalGraph](Yog.Builder.ToroidalGraph.md): A specialized grid graph result for toroidal (wrapping) grids.
- [Yog.Centrality](Yog.Centrality.md): Centrality measures for identifying important nodes in graphs.
- [Yog.Community](Yog.Community.md): Community detection and clustering algorithms.
- [Yog.Community.CliquePercolation](Yog.Community.CliquePercolation.md): Clique Percolation Method (CPM) for detecting overlapping communities.
- [Yog.Community.Dendrogram](Yog.Community.Dendrogram.md): Hierarchical community structure from algorithms like Louvain, Walktrap, Leiden.
- [Yog.Community.FluidCommunities](Yog.Community.FluidCommunities.md): Asynchronous Fluid Communities detection algorithm.
- [Yog.Community.GirvanNewman](Yog.Community.GirvanNewman.md): Girvan-Newman algorithm for hierarchical community detection.
- [Yog.Community.Infomap](Yog.Community.Infomap.md): Infomap community detection algorithm.
- [Yog.Community.LabelPropagation](Yog.Community.LabelPropagation.md): Label Propagation Algorithm (LPA) for community detection.
- [Yog.Community.Leiden](Yog.Community.Leiden.md): Leiden algorithm for community detection.
- [Yog.Community.LocalCommunity](Yog.Community.LocalCommunity.md): Local community detection using fitness maximization.
- [Yog.Community.Louvain](Yog.Community.Louvain.md): Louvain method for community detection.
- [Yog.Community.Metrics](Yog.Community.Metrics.md): Community quality metrics and graph statistics.
- [Yog.Community.Overlapping](Yog.Community.Overlapping.md): Result of overlapping community detection (e.g., Clique Percolation).
- [Yog.Community.Result](Yog.Community.Result.md): Result of community detection algorithms.
- [Yog.Community.Walktrap](Yog.Community.Walktrap.md): Walktrap algorithm for community detection.
- [Yog.Connectivity](Yog.Connectivity.md): Graph connectivity analysis - finding connected components, bridges, articulation points,
strongly connected components, and k-core decomposition.
- [Yog.Connectivity.Analysis](Yog.Connectivity.Analysis.md): Algorithms for analyzing graph connectivity (bridges, articulation points).

- [Yog.Connectivity.Components](Yog.Connectivity.Components.md): Algorithms for finding (weakly) connected components in graphs.

- [Yog.Connectivity.KCore](Yog.Connectivity.KCore.md): Algorithms for k-core decomposition.
- [Yog.Connectivity.SCC](Yog.Connectivity.SCC.md): Strongly Connected Components (SCC) algorithms.

- [Yog.DAG](Yog.DAG.md): Directed Acyclic Graph (DAG) data structure.
- [Yog.DAG.Algorithm](Yog.DAG.Algorithm.md): Algorithms for Directed Acyclic Graphs (DAGs).
- [Yog.DAG.Model](Yog.DAG.Model.md): Core DAG type and basic operations.
- [Yog.DisjointSet](Yog.DisjointSet.md): Disjoint Set Union (Union-Find) data structure for efficient set operations.
- [Yog.Flow.MaxFlow](Yog.Flow.MaxFlow.md): Maximum flow algorithms and min-cut extraction for network flow problems.
- [Yog.Flow.MaxFlowResult](Yog.Flow.MaxFlowResult.md): Result of maximum flow computation (Edmonds-Karp, etc.).
- [Yog.Flow.MinCut](Yog.Flow.MinCut.md): Global minimum cut algorithms for undirected graphs.
- [Yog.Flow.MinCutResult](Yog.Flow.MinCutResult.md): Result of minimum cut computation.
- [Yog.Flow.NetworkSimplex](Yog.Flow.NetworkSimplex.md): Minimum cost flow algorithms for network flow optimization.
- [Yog.Functional.Algorithms](Yog.Functional.Algorithms.md): Classic graph algorithms using purely functional inductive decomposition.
- [Yog.Functional.Analysis](Yog.Functional.Analysis.md): Structural analysis for inductive graphs — components, bridges, and articulation points.
- [Yog.Functional.Model](Yog.Functional.Model.md): Inductive graph representation based on Martin Erwig's
[Functional Graph Library](https://web.engr.oregonstate.edu/~erwig/fgl/) (FGL).
- [Yog.Functional.Model.Context](Yog.Functional.Model.Context.md): A node context containing the node's identity, label, and adjacency information.

- [Yog.Functional.Transform](Yog.Functional.Transform.md): Higher-order transformations for inductive graphs — map, filter, and structural changes.
- [Yog.Functional.Traversal](Yog.Functional.Traversal.md): Inductive graph traversals — BFS and DFS without explicit visited sets.
- [Yog.Generator.Classic](Yog.Generator.Classic.md): Deterministic graph generators for common graph structures.
- [Yog.Generator.Random](Yog.Generator.Random.md): Stochastic graph generators for random graph models.
- [Yog.Graph](Yog.Graph.md): Core graph data structure.
- [Yog.Health](Yog.Health.md): Network health and structural quality metrics.
- [Yog.IO.GDF](Yog.IO.GDF.md): GDF (GUESS Graph Format) serialization support.
- [Yog.IO.GraphML](Yog.IO.GraphML.md): GraphML (Graph Markup Language) serialization support.
- [Yog.IO.JSON](Yog.IO.JSON.md): JSON format import/export for graph data exchange.
- [Yog.IO.LEDA](Yog.IO.LEDA.md): LEDA (Library of Efficient Data types and Algorithms) graph format support.
- [Yog.IO.List](Yog.IO.List.md): Adjacency list import/export for graph serialization.
- [Yog.IO.Matrix](Yog.IO.Matrix.md): Adjacency matrix import/export for graph serialization.
- [Yog.IO.MatrixMarket](Yog.IO.MatrixMarket.md): Matrix Market (.mtx) format serialization support.
- [Yog.IO.Pajek](Yog.IO.Pajek.md): Pajek (.net) format serialization support.
- [Yog.IO.TGF](Yog.IO.TGF.md): Trivial Graph Format (TGF) serialization support.
- [Yog.MST](Yog.MST.md): Minimum Spanning Tree (MST) algorithms for finding optimal network connections.
- [Yog.Model](Yog.Model.md): Core graph data structures and basic operations for the yog library.
- [Yog.Multi](Yog.Multi.md): Unified facade for multigraph operations.
- [Yog.Multi.Eulerian](Yog.Multi.Eulerian.md): Eulerian path and circuit detection for multigraphs.
- [Yog.Multi.Graph](Yog.Multi.Graph.md): Multigraph with support for parallel edges.
- [Yog.Multi.Model](Yog.Multi.Model.md): Core multigraph type and basic operations.
- [Yog.Multi.Model.Graph](Yog.Multi.Model.Graph.md): A multigraph that can hold multiple (parallel) edges between nodes.

- [Yog.Multi.Traversal](Yog.Multi.Traversal.md): Traversal operations for multigraphs.
- [Yog.Operation](Yog.Operation.md): Graph operations - Set-theoretic operations, composition, and structural comparison.
- [Yog.Pathfinding](Yog.Pathfinding.md): Unified facade for pathfinding algorithms.
- [Yog.Pathfinding.AStar](Yog.Pathfinding.AStar.md): A* (A-Star) search algorithm for optimal pathfinding with heuristic guidance.
- [Yog.Pathfinding.BellmanFord](Yog.Pathfinding.BellmanFord.md): Bellman-Ford algorithm for single-source shortest paths with negative weight support.
- [Yog.Pathfinding.Bidirectional](Yog.Pathfinding.Bidirectional.md): Bidirectional search algorithms that meet in the middle for dramatic speedups.
- [Yog.Pathfinding.Dijkstra](Yog.Pathfinding.Dijkstra.md): Dijkstra's algorithm for single-source shortest paths.
- [Yog.Pathfinding.FloydWarshall](Yog.Pathfinding.FloydWarshall.md): [Floyd-Warshall algorithm](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm)
for all-pairs shortest paths in weighted graphs.
- [Yog.Pathfinding.Johnson](Yog.Pathfinding.Johnson.md): [Johnson's algorithm](https://en.wikipedia.org/wiki/Johnson%27s_algorithm) for
all-pairs shortest paths in weighted graphs with negative edge weights.
- [Yog.Pathfinding.Matrix](Yog.Pathfinding.Matrix.md): Optimized distance matrix computation for subsets of nodes.
- [Yog.Pathfinding.Path](Yog.Pathfinding.Path.md): Result of pathfinding algorithms (Dijkstra, A*, BFS, etc.).
- [Yog.Pathfinding.Utils](Yog.Pathfinding.Utils.md): Shared types and utilities for pathfinding algorithms.

- [Yog.PriorityQueue](Yog.PriorityQueue.md): A Priority Queue implementation based on Pairing Heap.
- [Yog.Property](Yog.Property.md): Unified facade for assessing graph structures and invariant properties.
- [Yog.Property.Bipartite](Yog.Property.Bipartite.md): [Bipartite graph](https://en.wikipedia.org/wiki/Bipartite_graph) analysis and matching algorithms.
- [Yog.Property.Clique](Yog.Property.Clique.md): [Clique](https://en.wikipedia.org/wiki/Clique_(graph_theory)) finding algorithms using the
[Bron-Kerbosch algorithm](https://en.wikipedia.org/wiki/Bron%E2%80%93Kerbosch_algorithm).
- [Yog.Property.Cyclicity](Yog.Property.Cyclicity.md): Graph [cyclicity](https://en.wikipedia.org/wiki/Cycle_(graph_theory)) and
[Directed Acyclic Graph (DAG)](https://en.wikipedia.org/wiki/Directed_acyclic_graph) analysis.
- [Yog.Property.Eulerian](Yog.Property.Eulerian.md): [Eulerian path](https://en.wikipedia.org/wiki/Eulerian_path) and circuit algorithms using
[Hierholzer's algorithm](https://en.wikipedia.org/wiki/Eulerian_path#Hierholzer's_algorithm).
- [Yog.Property.Structure](Yog.Property.Structure.md): Structural properties of graphs.
- [Yog.Render.ASCII](Yog.Render.ASCII.md): ASCII art rendering for grid graphs - quick visualization in terminal output.
- [Yog.Render.DOT](Yog.Render.DOT.md): DOT (Graphviz) format export for visualizing graphs.
- [Yog.Render.Mermaid](Yog.Render.Mermaid.md): Mermaid.js format export for embedding diagrams in web pages and documents.
- [Yog.Transform](Yog.Transform.md): Graph transformations and mappings - functor operations on graphs.
- [Yog.Traversal](Yog.Traversal.md): Graph traversal algorithms - systematic exploration of graph structure.
- [Yog.Traversal.Cycle](Yog.Traversal.Cycle.md): Cycle detection algorithms for directed and undirected graphs.

- [Yog.Traversal.Implicit](Yog.Traversal.Implicit.md): Implicit graph traversal — BFS, DFS, and Dijkstra on graphs defined by successor functions
rather than materialized data structures.

- [Yog.Traversal.Sort](Yog.Traversal.Sort.md): Topological sorting algorithms — Kahn's algorithm and lexicographic variant.

- [Yog.Traversal.Walk](Yog.Traversal.Walk.md): Graph walking algorithms — BFS and DFS traversals with fold support and path finding.

- [Yog.Utils](Yog.Utils.md): Shared utility functions used across the Yog library.