Information Structure Choices
In this section we discuss various ways of representing directed graphs, the different
shapes that their entity models can take and the different organisations of information
implied by the different shapes.
There is a reliance here, in this presentation, on the use of the work ‘abstract’
and
on an understanding of what the mathematician means by this.
The best that I can offer as explanation is that the mathematical idea of an abstract
structure
is that of a set of individuals and relations independent of any particular
representation of the individuals and the mathematical concepts of
graph and
directed graph are cases in point.
In the case of a graph the individuals are notionally
vertices and edges and the relations are the
incidence relations between them. It is certainly ironic and perhaps at first sight
paradoxical, but with regard to any particular
abstract structure, to describe it we need
some kind
of representation even though what we seek to describe is something
without any particular representation. Mathematican Robin Gandy describes this to a nonmathematical
audience in
a lecture
‘Structure in Mathematics’
^{1}; he draws the love
relationships to be found in Iris Murdoch's novel Severed Head as a
directed graph and I have drawn an equivalent graph in figure
10
.
If we abstract a directed graph from this then there are no labels, no lines,
no points on paper just the facts of a set of notional individual entities and ther
relationships between them
^{2}.
pLh

hLp

aLp

pLa

pLg

mLp

mLh

aLx

xLa

gLx

gLm

mLg

Table 1
Gandy's relational depiction of the same love relationships.
As an illustration of different representations of the same abstract structure,
Gandy gives the relational representation shown in table
1
.
In the relational representation,
p occupies the same structural position as
PALMER,
h as
HONOR,
a as
ANTONIA,
g as
GEORGIE,
m as
MARTIN,
x as
ALEXANDER.
This relational description can be described by the message structure:
Gandy's depicted love relationship is a manymany relationship and we can represent
in an entity model like this:
There is of course nothing special about this
example
—
loves is a recursive manymany
relationship and
any such could be used to illustrate that a recursive manymany relationship is structurally
a directed graph.
Gandy's relational representation shown in figure 10
could be rearranged in
two ways
—
from the point of view of the lover or the loved; these are shown in figures 11
and
12
.
But what communication structure do we associate with this? Well, this way of modelling
directed graphs is akin to the matrix structure modelled in chapter one.
Applied to the representation of the Severed Head love relationships it implies a
communication in which
it is apparent both (i) who loves each subject
a,
g,
h and so on and (ii) who each subject
a,
g,
h, etc.
is loved by. This is made apparent by a matrix representation:

a

g

h

m

p

x

a





x

x

g




x

x


h




x

x


m







p

x

x

x

x



x

x

x




