OutdestIndexn

OutdestIndexn is a function-like notion used in theoretical discussions of multi-output nodes in graphs and dataflow systems. It denotes the index of the nth outgoing destination from a given source node.

Definition and scope. For a directed graph G=(V,E) where every node s has an ordered list of outgoing destinations Out(s) = [d1, d2, ..., dk], with each di in V, outdestIndexn(s) returns the nth element of Out(s). In other words, it identifies the destination node reached by the nth outgoing edge from s. If edges carry additional metadata or if a numeric edge identifier is required, the function may instead return the corresponding edge identifier or a composite record.

Properties. The function is deterministic when n is within the valid range 1 to k (or 0 to k-1 in zero-based indexing). The value depends on the predefined order of the outgoing edges for s. The term outdegree(s) refers to the number k, the number of outgoing edges from s. If n is outside the valid range, outdestIndexn is typically undefined or may raise an exception, depending on the formalism used.

Use cases and applications. The concept is used in routing decisions, scheduling in dataflow graphs, and compiler intermediate representations where nodes can yield multiple results or paths. It provides a concise way to reference the n-th successor in a fixed ordering, aiding analysis and transformations that depend on edge order rather than just connectivity.

Example. If Out(s) = [A, B, C], then outdestIndex2(s) = B (using one-based indexing). With zero-based indexing, outdestIndex1(s) = B. If n exceeds the number of outgoing edges, the lookup is undefined.

Implementation notes. In practice, outdestIndexn can be realized as a direct array or list access, yielding O(1) time, provided the outgoing edges are stored in a stable, indexed order.