In fact, what I say below isn't quite precise. It is true of 
'minimal' rings in planar graphs when you are counting the discrete 
'faces' enclosed by each ring - and this is the natural architectural 
way to think of rings - but it's not of course true of all possible 
rings in the graph, many of which will be non-minimal.

Thanks to Roy Wagner for drawing my attention to this ! - Bill


It's simpler than that ! Ringiness is connectivity. Construct a tree 
graph (without rings) with k nodes. It will have k-1 links, 
regardless of what kind of tree (say deep or shallow) it is. Then 
every link you add that does not repeat an existing link will create 
a ring - and exactly one ring. So ringiness expresses the 
connectivity of the whole graph. - Bill

At 21:26 10/08/2009, you wrote:
>Erica,
>
>There are a couple of other answers to the question of why these
>measures seem to have fallen out of fashion:
>
>1. they tend to have dropped off the list of measures being taught on
>the MSc Advance Architectural Studies at UCL, mainly due to a lack of
>time, since other kinds of measure have shown themselves to be really
>empirically interesting - that doesn't mean that ringiness is
>unimportant - quite the opposite - the measures of choice and control
>value are both essentially measures of ringiness, and under the new
>'angular segmental' analysis choice measures have shown a resurgence
>of ability to explain empirical phenomena;
>
>2. the more popular measures are those that distinguish between
>different parts of a system. Relative ringiness is a measure of the
>ringiness of a whole system (a single number is a characteristic of
>the whole).  The measure of relative ringiness is used primarily when
>you are trying to compare a sample of 'whole systems' - eg. in
>analysis of a large sample of house plans. Both control and choice are
>measures of ringiness that can be used to try and explain variations
>between one part of a system and another.
>
>By the way, and as an aside, I think Lucas is wrong to suggest that
>the syntax field suffers from poor use of statistics. In my
>experience, in our kind of field, syntax does at least DO statistics.
>Most other persuasions don't even have methods to represent the object
>they are interested in, let alone to quantify the morphology of
>interest, and consequently cant even suffer from poor use of
>statistics. Granted the statistics that tend to be used are relatively
>simple and unsophisticated, but simple statistics are often the most
>appropriate for the purpose.
>
>Alan
>
>
>On 10 Aug 2009, at 19:58, Lucas Figueiredo wrote:
>
>>Dear Erica,
>>
>>Space syntax has always suffered of a (very) poor use of statistics,
>>which is understandable in a field populated by people with such
>>diverse background. This might have influenced the use of a few
>>measures for the reasons you mentioned (poor correlations, etc.),
>>which are not necessarily problems of the measures per se, but
>>(probably) of the treatment given to them.
>>
>>The other reason is that most of the software available now use
>>distance-based models, such as Angular-Segment-Analysis, which have a
>>different theoretical-and-methodological basis, one that does not
>>really focus on graph-structures but on a interpretation of how
>>individuals navigate and read the system.
>>
>>However, measures of ringness are still some of the most important in
>>network science/graph theory. The clustering coefficient, for
>>instance, is a measure of ringness - reflecting the number of
>>triangles. There are versions for the number of squares (grid
>>coefficients) - which make more sense for cities. I have some comments
>>here:
>>http://eprints.ucl.ac.uk/2694/
>>
>>I found later that both kinds of coefficient suffer of size effects
>>and it is often better to use the raw number of triangles or squares.
>>I have used them to create classifications of cities.
>>
>>Ringness, in general, reflects the local interconnectivity between
>>spaces, lines or whatever a node represents. I found, for instance,
>>that the number of squares (rings of 3 steps) reflects grid
>>intensification and identifies the same "patches" that metric-based
>>measures from Angular Analysis identify.
>>
>>Unfortunately, I am not sure if there is space syntax software
>>available that use/implement them. Perhaps, if you are working with
>>small systems, you could use other kind network/graph software, but
>>none comes to my mind at the moment.
>>
>>Best Regards,
>>Lucas Figueiredo
>>
>>On 10/08/2009, Erica Calogero <[log in to unmask]> wrote:
>>>Hi there,
>>>
>>>This is a question to the old timers and software developers as
>>>well as
>>>current practitioners (AKA everybody)....
>>>
>>>What happened to measures of ringyness that were used in early (SLoS)
>>>analyses? Justin de Syllas' 1981 thesis refers to relative
>>>ringyness or R.R.
>>>otherwise known as distributedness. When and why was this measure
>>>abandoned
>>>or not implemented in the software? Was it found to be unreliable,
>>>replaced
>>>by another measure that measured the same thing, not found to
>>>correlate
>>>statistically with any experimental observations? Or another more
>>>prosaic
>>>reason? I would love to know what happened to it, and also the use
>>>of A,B,C
>>>and D space classifications. So if any current practitioners or
>>>software
>>>developers are using or have implemented any of these measures in
>>>their
>>>software or practice I would love to know.
>>>
>>>Kind regards,
>>>
>>>Erica Calogero.
>>>
>>>EngD student.
>>
>>
>>--
>>Lucas Figueiredo