# directed path

## directed path

[də¦rek·təd ′path]
(mathematics)
A sequence of vertices, v 1, v 2, … v n, in a directed graph such that there is an arc from vi to vi +1 for i = 1, 2, …, n-1. Also known as dipath.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Considering the directed fuzzy relation, we define the concept of directed fuzzy social networks and develope some concepts such as fuzzy directed walk, fuzzy directed trail, fuzzy directed path, and fuzzy semipath for directed fuzzy social network.
We will focus on the most important directed fuzzy social network concepts including the fuzzy directed walk, fuzzy directed trail, fuzzy directed path, and fuzzy semipath.
A fuzzy directed path in a directed fuzzy social network is a fuzzy directed walk in which no actor and no fuzzy relation is included more than once.
In Figure 1, [??] = [v.sub.5][v.sub.1][v.sub.2][v.sub.3][v.sub.4][v.sub.2][v.sub.3] is a fuzzy directed walk, [??] = [v.sub.5][v.sub.4][v.sub.2][v.sub.3][v.sub.4] fuzzy directed trail, [??] = [v.sub.5][v.sub.1][v.sub.2][v.sub.3][v.sub.4] fuzzy directed path, and [??] = [v.sub.1][v.sub.5][v.sub.4][v.sub.3][v.sub.2] a fuzzy semipath.
However, in order to define reachability in a directed fuzzy social network, we must consider fuzzy directed paths. Specifically, if there is a fuzzy directed path from [v.sub.i] to [v.sub.j], then [v.sub.j] is reachable from [v.sub.i].
(2) fuzzy unilaterally connected if they are joined by a fuzzy directed path from [v.sub.i] to [v.sub.j], or a fuzzy directed path from [v.sub.j] to [v.sub.i],
(3) fuzzy strongly connected if there is a fuzzy directed path from [v.sub.i] to [v.sub.j] and a fuzzy directed path from [v.sub.j] to [v.sub.i]; the path from [v.sub.i] to [v.sub.j] may contain different actors and fuzzy relations than the path from [v.sub.j] to [v.sub.i],
In a fuzzy unilaterally connected directed fuzzy social network, between each pair of actors there is a fuzzy directed path from one actor to the other; in other words, at least one actor is reachable from the other in the pair.
According to the calculated result in Step 3, the numbers of unidirectional fuzzy structural holes that vk occupies are fus([v.sub.k]) = ([[summation].sup.m.sub.i=1] [p.sub.i] x [q.sub.i]) - u, where u is the repetitive computation numbers of unidirectional fuzzy structural holes on the fuzzy directed path [[bar.[omega]].sub.i].
Consider now both fuzzy directed paths and fuzzy semipaths between pairs of actors.
In a directed fuzzy social network [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], seek the fuzzy directed paths [[bar.[omega]].sub.i] (i = 1,2, ..., m), which is through [v.sub.k], and the actors are not less than 3.
In this volume, Grandis (mathematics, University of Genoa) explores the new field of directed algebraic topology, which is distinguished from classical algebraic topology by the principle that directed spaces have privileged directions and directed paths in these spaces need not be reversible.

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