The phrase "a path directed from" is correct and usable in written English.
It can be used in contexts discussing directions, processes, or relationships between elements, often in technical or metaphorical discussions.
Example: "The algorithm establishes a path directed from the input data to the output results."
Alternatives: "a route originating from" or "a pathway leading from".
In contrast, the strongly connected component (SCC) is defined as subnetwork that connects each pair of genes in both directions that means for each pair of genes A and B there exists a directed path from gene A to gene B but also a directed path from gene B to gene A. The TRN consists of two strongly connected components.
If x, y are vertices of the digraph G, then a directed path from x to y of length N is a sequence { x i } i = 0 N of N + 1 vertices such that x 0 = x, x N = y and ( x i, x i + 1 ) ∈ E ( G ), i = 0, 1, …, N. A closed directed path of length N > 1 from x to y, i.e., x = y, is called a directed cycle.
A network is called strongly connected if for every two nodes A and B there is a directed path from A to B and vice versa.
For each distinct pair of nodes A and B in G, we say that A ≪ B if there exists a directed path from A to B within G.
We say that A ≪ B if there exists at least one directed path from A to B. There always exists a trivial directed path from any node to itself so that A ≪ A is true for any node A in G.
An arc (a, b) is redundant if there is a directed path from a to b that that does not utilize this arc.
We say that a pair [ a, b] ∈ P is satisfied by a given orientation G → if there exists a directed path from a to b in G →.
For every subset U ⊆ S ⧹ { r } and for each customer k ∈ R, an open arc from a facility in U toward j, necessitates a directed path from r towards U. Constraints (2) can be replaced by inequality in case that c ij ≥ 0, for all ij ∈ A R. Furthermore, the same optimization problem with continuous assignment variables x ij, for all ij ∈ A R, returns an optimal ConFL solution.
(Consequently there is an accessibility condition for the designated element: if one thinks of the extensional relation as a graph, there must be a directed path from any element to the designated element).
For example, the edge set (A → B, B → C,..., Y → Z), form a directed path from node A to node Z.
