Acyclic graph
An acyclic graph is a graph that contains no cycles.
Optimization Algorithms: AI techniques for design, planning, and control problems
An acyclic graph is a graph that contains no cycles.
- How it is used
- Uses directed acyclic graphs to represent task dependencies and precedence constraints in scheduling.
- How deep it goes
- Defines cycles and acyclic graphs, demonstrates construction and verification, and stops short of explaining internal detection algorithms.
- Examples
- Demonstrates a five-node directed graph in NetworkX and relates acyclic structure to task-scheduling dependencies.
- What you can do after
- Operate/configure NetworkX to create a directed graph and check whether it is acyclic.
Grokking Data Structures
An acyclic graph is a graph that contains no cycles.
- How it is used
- Uses acyclicity to characterize graph structure and support cycle detection and topological sorting.
- How deep it goes
- Defines paths and cycles, then gives a colored-vertex DFS procedure; defers other applications to advanced treatment.
- Examples
- Uses an animal follower graph and an iterative stack-based DFS implementation with white, gray, and black vertex states.
- What you can do after
- Diagnose cycles in a directed graph using depth-first search and vertex-color tracking.
Graph Neural Networks in Action
An acyclic graph is a graph containing no cycle that returns to a starting node without backtracking.
- How it is used
- Frames non-looping structure for causal analysis, workflow processes, dependency chains, and other one-way relationships.
- How deep it goes
- Defines cycles, contrasts directed and undirected forms, and stops short of implementation or cycle-detection procedures.
- Examples
- Uses a visual comparison of a cyclic graph, an undirected acyclic graph, and a DAG.
- What you can do after
- Evaluate whether a graph permits cycles and recognize when directed one-way structure forms a DAG.
Read how Graph Neural Networks in Action explains acyclic graph →
Related concepts
- graphkind of · A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
- treeincludes · A tree is a connected, acyclic structure of nodes, commonly organized hierarchically through parent-child relationships and optionally around a designated root.
- directed acyclic graphincludes · A directed acyclic graph is a graph with directed edges and no directed cycles.
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