DAGraphsien

DAGraphsien is a theoretical construct in graph theory used to model directed acyclic graphs (DAGs) augmented with labeling, layering, and constraint rules that support deterministic scheduling and dataflow analysis. The term combines the standard DAG formalism with a stylized suffix to indicate a specialized class intended for computational modeling.

In a DAGraphsien, each node carries a type and a set of attributes. Node types typically include data inputs, operations, and control operators. Edges represent dependencies and are annotated with metadata such as weight, delay, or resource requirements. A layering function assigns a nonnegative integer to each node, and all edges are constrained to go from lower to higher layers, which guarantees acyclicity and provides a topological ordering.

Key properties include acyclicity by construction, the existence of a unique topological sort when layerings are respected, and the ability to compute a critical path length and other workflow metrics. DAGraphsien graphs support standard DAG algorithms for reachability, scheduling, and parsing, with extensions to handle annotated edges and layered evaluation.

Variants may allow limited conditional branching through specialized control nodes or virtual edges, while preserving the overall DAG structure. This enables modeling of deterministic workflows, such as data processing pipelines, build systems, and task orchestration tools.

Example: a small DAGraphsien with data node A, operation nodes B and C depending on A, and a final node D depending on B and C, where the layers are A(0) -> B(1), C(1) -> D(2).