Yes: if you can sort your connection matrix so it is upper triangular, you can also sort it so that it is lower triangular.
-- Raul On Wed, Mar 21, 2012 at 10:48 AM, Devon McCormick <devon...@gmail.com> wrote: > So Raul, according to what you said > > On Wed, Mar 21, 2012 at 9:25 AM, Raul Miller <rauldmil...@gmail.com> wrote: > ... >> I should also note that a "directed acyclic graph" means that the data >> can be sorted such that the connection matrix is lower-triangular. > > I think that answers my question below about whether my example is a > DAG - if I swap the labels for nodes 3 & 5, the adjacency matrix would > be triangular, though upper-triangular which I assume is conceptually > the same (because we can convert one to the other by swapping node "n" > with "5-n"). > > NB.* egDAG: example picture of a directed acyclic graph with the > NB. characters "V>" (and, potentially, "^<") representing directional > NB. arrowheads; "V>" together means a split both down and to the right. > egDAG=: 0 : 0 > 0->2->5 > | | > | V > V>--->4 > | > V > 1 > | > V > 3 > ) > NB. Is this a DAG if you can reach "4" by two different paths? > > NB. The picture above corresponds to this adjacency matrix representation. > amDAGeg=: ".&><;._2 ] 0 : 0 > 0 1 1 0 0 0 > 0 0 0 1 0 0 > 0 0 0 0 0 1 > 0 0 0 0 0 0 > 0 0 0 0 0 0 > 0 0 0 0 1 0 > ) > > NB. Vertex Array representation of same graph as above. > vaDAGeg=: ,&.>(1 2);(3);(5);(i.0);(i.0);<4 > > NB. A (nodes);(edges) representation of the above DAG. > neDAGeg=: (0 1 2 3 4 5);<|:0 1,0 2,1 3,2 5,:5 4 > > -- > Devon McCormick, CFA > ^me^ at acm. > org is my > preferred e-mail > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
