# [R] Add transitivity to a matrix?

Eric Berger er|cjberger @end|ng |rom gm@||@com
Tue Jun 18 15:01:55 CEST 2019

```Very nice, Peter.
Here is one version of Peter's suggestion expressed in R code

M <- M | t(M)  # first step as symmetric matrix as stated by OP
Q <- M
for ( i in 2:(ncol(Q)-1) )
Q <- Q + Q %*% M

R <- (Q > 0)
R

HTH,
Eric

On Tue, Jun 18, 2019 at 12:46 PM peter dalgaard <pdalgd using gmail.com> wrote:

> Sounds like this is isomorphic to reachability in graph theory. I wonder
> if
>
> (sum_1^n M^i) > 0
>
> would suffice?
>
> -pd
>
>
>
> > On 18 Jun 2019, at 02:08 , Duncan Murdoch <murdoch.duncan using gmail.com>
> wrote:
> >
> > On 17/06/2019 7:34 p.m., Bert Gunter wrote:
> >> Depends on what you mean by "simple" of course, but suppose that:
> >> M[i,j] & M[j,k] & M[k,n] are TRUE and M[i,k] and M[i,n] are FALSE.
> >> Then the procedure would see that M[i,k] needs to change to TRUE, but
> not that M[i,n] needs to also become TRUE *after* M[i,k] changes.  This
> seems to imply that an iterative solution is necessary.
> >
> > Right, that's a good point.
> >
> > Duncan Murdoch
> >
> >> One such procedure, via repeated matrix multiplication to check for and
> impose transitivity, appears to be suggested by this discussion:
> >>
> https://math.stackexchange.com/questions/228898/how-to-check-whether-a-relation-is-transitive-from-the-matrix-representation
> >> Cheers,
> >> Bert
> >> On Mon, Jun 17, 2019 at 10:29 AM Duncan Murdoch <
> murdoch.duncan using gmail.com <mailto:murdoch.duncan using gmail.com>> wrote:
> >>    On 17/06/2019 1:19 p.m., Duncan Murdoch wrote:
> >>     > Suppose I have a square logical matrix M which I'm thinking of as
> a
> >>     > relation between the row/column numbers.
> >>     >
> >>     > I can make it into a symmetric relation (i.e. M[i,j] being TRUE
> >>    implies
> >>     > M[j,i] is TRUE) by the calculation
> >>     >
> >>     > M <- M | t(M)
> >>     >
> >>     > Is there a simple way to ensure transitivity, i.e. M[i,j] &
> >>    M[j,k] both
> >>     > being TRUE implies M[i,k] is TRUE?
> >>     >
> >>     > The operation should only change FALSE or NA values to TRUE
> >>    values; TRUE
> >>     > values should never be changed.
> >>    I also want the changes to be minimal; changing everything to TRUE
> >>    would
> >>    satisfy transitivity, but isn't useful to me.
> >>    Duncan Murdoch
> >>    ______________________________________________
> >>    R-help using r-project.org <mailto:R-help using r-project.org> mailing list --
> >>    To UNSUBSCRIBE and more, see
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> >>    and provide commented, minimal, self-contained, reproducible code.
> >>
> >
> > ______________________________________________
> > R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
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> > and provide commented, minimal, self-contained, reproducible code.
>
> --
> Peter Dalgaard, Professor,
> Center for Statistics, Copenhagen Business School
> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Office: A 4.23
> Email: pd.mes using cbs.dk  Priv: PDalgd using gmail.com
>
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