downfromnode

Downfromnode is a term used in graph processing to describe an operation that collects all nodes reachable from a designated starting node by following directed edges in a downward direction, from parent toward child. In trees and directed acyclic graphs this typically yields the subgraph rooted at the starting node. When cycles exist, implementations usually maintain a visited set to avoid infinite traversal.

Inputs and outputs: Given a directed graph G=(V,E), a start node s, and an optional depth limit, the downfromnode operation returns the set of nodes reachable from s within that limit, along with the edges among them. Variants may return only the node set, or the induced subgraph, or a collection of paths from s to each reachable node. A common option is to exclude the starting node, depending on whether the root is considered part of the subtree.

Traversal methods: Depth-first search and breadth-first search are standard implementations. DFS explores long descendant chains first, while BFS expands layer by layer. Depth limits, property-based filtering, and edge restrictions can tailor the result to specific applications. Handling cycles typically requires a visited structure to ensure termination.

Complexity and properties: The running time is proportional to the number of reachable nodes and edges among them, O(R + E_R), with space complexity O(R) for the visited set and the resulting subgraph. The operation is well-defined for trees and DAGs, and its behavior can depend on whether the starting node is included in the output or the traversal depth is restricted.

Applications and relation: Downfromnode is used for subtree extraction, visualization, dependency analysis, and query processing where descendant enumeration is needed. Related concepts include descendants, downstream reachability, and standard graph traversals such as DFS and BFS. In practice, the exact semantics may vary by library, so API documentation should be consulted for specifics.