Flowsto

Flowsto is a term used in graph theory, network modeling, and static data-flow analysis to denote a directional transfer of flow from one element to another. It is typically defined as a binary relation on the nodes of a directed graph G = (V, E), often written as flowsTo ⊆ V × V. In many contexts flowsTo is taken as the transitive closure of the edge relation, so that a flowsTo b if there exists a directed path from a to b; in other contexts it may be restricted to immediate successors via a single edge.

Properties commonly associated with flowsTo include that the relation is not inherently symmetric and becomes reflexive if zero-length paths are allowed, and transitive by construction when using paths. In graphs with cycles, flowsTo can relate nodes in both directions, reflecting the presence of cycles.

Applications of flowsTo span several disciplines. In network and supply-chain modeling, flowsTo expresses reachability or potential transfer of goods or information from one node to another, aiding in routing and containment analysis. In program analysis and software engineering, flowsTo describes how values or tainted data may propagate through variables and program points, underpinning data-flow analyses, taint tracking, and points-to analyses. It also serves as a conceptual tool for understanding dependency and propagation in systems and workflows.

Limitations include that flowsTo captures only the possibility of transfer, not quantity, capacity, cost, or timing. For quantitative modeling, flowsTo is often augmented with edge labels or numerical flow constraints and combined with optimization or timing analyses.