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Osman and Suliman

This document discusses the space syntax methodology, which analyzes building floor plans mathematically to reveal cultural norms. While acknowledging its contributions, the document identifies several limitations of the methodology. It notes that calculating shortest paths assumes a Western cultural perspective. The binary coding system leaves out various real-world spatial connections. And the methodology cannot stand alone and needs to be supplemented with socio-cultural research to fully interpret results. The document proposes ways to address these shortcomings and improve the methodology.

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0% found this document useful (0 votes)
118 views15 pages

Osman and Suliman

This document discusses the space syntax methodology, which analyzes building floor plans mathematically to reveal cultural norms. While acknowledging its contributions, the document identifies several limitations of the methodology. It notes that calculating shortest paths assumes a Western cultural perspective. The binary coding system leaves out various real-world spatial connections. And the methodology cannot stand alone and needs to be supplemented with socio-cultural research to fully interpret results. The document proposes ways to address these shortcomings and improve the methodology.

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Sha Ocampo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Arch. & Comport. /Arch. & Behav., Vol. 10, no 2, p.

189 - 204 189

The Space Syntax Methodology: Fits and Misfits

Khadiga M. Osman and Mamoun Suliman


College of Architecture
University of Florida
USA - Gainville, FL 32614-1563
and
Department of Electronics Engineering,
Sudan University of Science and Technology,
Khartoum,
Sudan

Abstract
The corner stone of the space syntax methodology is a simple mathematicallgraph
theory procedure intended to analyze nodal diagrams of plans to arrive at cultural
norms behind the morphology of buildings. Beside giving credit to the technique,
this paper discusses, with examples, its major shortcomings: the Western cultural
element in the calculation of the shortest path; the limitation of the inherent binary
coding; and the inability of the method to stand by itself, hence the necessity to
complement its findings with socio-cultural research.

Rbume
La mkthode de la syntaxe spatiale consiste en une simple procCdure mathkmatico-
graphique dans laquelle des diagrammes nodaux de plans sont examinks pour cerner
les normes culturelles qui soustendent la morphologie des b2timents. L'article for-
mule une apprkciation de cette technique, y compris de ses limites: l'influence de la
culture occidentale sur les calculs; les restrictions posCes par son codage binaire; et le
fait que la mCthode ne peut Stre utiliske seule puisque ses rksultats doivent Ctre
complktks par une recherche de type socio-culturel.

1. Introduction
The space syntax (Hillier and Hanson 1984 & 1987) is a theory and method for
investigating society-space relation. The main theoretical argument is founded on
the authors' assertion that building forms are embodied in social norms of societies.
Thus, according to its authors, analyzing and interpreting spatial qualities of artifacts
would reveal the social rules that regulate the interface among people. The analytical
190 Khadiga M. Osman and Mamoun Suliman

procedure is based on graphic representation, nodes and links, of traditional


architectural floor plans and the qualification of graph properties using mathematical
formulae. Although the analytical procedure of the method is simple, objective, and
replicable, the interpretation process of the numerical results remains complex, sub-
jective, and so controversial. In other words, the method does not seem to yield
much of the full scope of interpretation outlined by the pioneers, that is the unrave-
ling of social norms behind the morphology of buildings. On the contrary, wrong
interpretations, sometimes departing far from reality, might arise, as this paper will
demonstrate. Moreover, applying space syntax, while overlooking social and psy-
chological aspects of people, lead researchers to speculate and generalize about
social rules that produce shared design features.
The space syntax offers a significant contribution to the advancement of research in
the field of environmental design. Most important, it is the first research method in
the field that allows researchers to rely on objective concepts instead of on those
offered by the social sciences. Yet, in this paper we argue that regardless of the
advantages gained by applying space syntax, there are limitations to the method
which question its findings and interpretations. For instance, the way the shortest
path between any two internal nodes - which is essential for the derivation of the
main syntactic integration parameters - is calculated, makes the method inappro-
priate for the analysis of non-western houses. Also, the use of binary coding, one for
the direct connection between a pair of spaces and zero for the absence of direct
connectivity, leaves out various types of spatial, visual, auditory, and olfactory
connectivity which in reality can exist between two spaces. These limitations among
others are the subject of discussion in this paper. Furthermore, the paper proposes
alternative ways to rectify the shortcomings of the method and supplement its proce-
dures.

2. The Space Syntax


In "The Social Logic of Space," Bill Hillier and Julienne Hanson (1984) argue for
the considerable influence of socio-cultural norms on the spatial organization of
buildings. The authors (see also 1987) present an analytical method, "space syntax",
for reading, quantifying, describing, and comparing morphological patterns of buil-
dings for the purpose of projecting the social norms of their inhabitants. The basic
analytical procedure of the space syntax method is composed of the following two
steps.
First, traditional scaled architectural floor plans are transformed to a dimension-less
form of permeability diagrams or graph representation. Every habitable space in a
plan is to be subdivided into the largest and fewest convex spaces. The resulting
convex spaces, known as the convex map, which may or may not correspond to the
way in which the building is actually conceptualized, are represented by nodes and
the connection between them by lines. Nodes are then aligned above a "root" node
- that usually represents the outside space of a building - in levels, according to
The Space Syntax Methodology: Fits and Misfits 191

the number of spaces to be crossed to reach each convex space from the outside, or
the reverse.
Second, from the permeability diagram, the basic syntactic parameters - integra-
tion, connectivity, and control - are quantified. Values for all space syntax measu-
rements are calculated manually for simple graphs or generated by a computer pro-
gram for complex ones. Input to the computer is given as a matrix of connections
based on permeability diagrams. The key syntactic properties measured following
this procedure are the depth, shortest path, and the degree of ringiness. The shortest
path between a pair of nodes in a graph is defined as the minimum number of steps
taken to reach one node from the other, while the degree of ringiness or distributed-
ness is a measure of the existence of alternative routes between any pair of nodes.
These two properties are combined to develop a quantitative mathematical measure-
ment known as the integration or relative asymmetry value (RA). RA values are then
adjusted between theoretical and empirical limits to allow direct comparisons across
patterns regardless of their size. The adjusted integration measurement is known as
the Real Relative Asymmetry (RRA). Integration values range from 0 to 1. Low
values indicate integration and high values indicate segregation (for the definitions
and mathematical formulae of these syntactic measurements, consult Appendix I).

3. The Advantages of the Space Syntax


There are numerous benefits to be gained from the abstraction of architectural floor
plans into graphs of nodes and connections as suggested by the method. Among
them, the procedure offers easy, and well defined steps for the analysis, description,
and hence the comparison of buildings - though in a two dimensional form - and
their spatial qualities. Using space syntax procedure, it is easy to analyze floor plans
of buildings to reveal their underlying morphological structure. Subsequently, pro-
minent physical qualities that may dictate the use of buildings in certain ways might
be deduced. Furthermore, the method provides an opportunity "to switch problems
from one naturally-occurring mode to another where solutions may be more easily
obtained," write Haggett and Chorley (1969: 7). By transforming building plans into
graphs, environmental design researchers are able to utilize the powerful resources of
graph theory and matrix algebra to tackle various problems with great flexibility.
Last, but not least, it is a credit to the pioneers that space syntax has opened the door
to promising modification and development effort that will enhance and thus
strengthen the method's analytical and interpretation procedures; this paper aims to
contribute in this effort.

4. The Limitations of the Space Syntax


Presently, more than a decade since space syntax was first published, 1 and after being
widely used in the analysis of various types of building patterns, the validity of the

The most inclusive publication that presents the full theoretical argument as well as the analytical procedure of the
space syntax is the "Social Logic of Space," by Hillier and Hanson, published in 1984. Before that, Bill Hillier and his
192 Khadiga M. Osman and Mamoun Suliman

technique still remains controversial, not having yet been fully investigated by
architectural researchers. The most noted review,2 by an architect, is the criticism of
Lawrence (1990) which briefly outlines the inadequacy of the technique, as it exists,
in projecting society's norms. Similar remarks were made by some social science
researchers. Edmund Leach (1978: 397), for example, argues:
"From my point of view the syntactic argument is meaningful and interesting, but I
do not believe that one can immediately infer the generative syntax simply by loo-
king at the lay-out of settlement patterns on the ground, and even if one could be sure
of what the generative syntactic rules have been, one cannot infer anything at all
about the society that makes use of the resultant settlement."
The authors here, in agreement with both Lawrence and Leach, believe that "without
knowing the facts," a two-dimensional floor plan is an insufficient source for infer-
ring social dimensions of societies. This paper goes a further step beyond the criti-
cism of other researchers in pointing out some problems associated with the tech-
nique and with the mechanics of its application, and in proposing some remedies.

4.1. The cross-cultural invalidity of the method


The theory of the space syntax defines a building, abstractly, as
"a certain ordering of categories, to which is added a certain system of controls, the
two conjointly constructing an interface between the inhabitants of the social know-
ledge embedded in the categories and the visitors whose relations with them are
controlled by the building," (Hillier and Hanson, 1984: 147).
Based on the above argument, the configuration of any building is conceptualized by
the theory of the space syntax as the relationship among the inner spaces of that buil-
ding and its immediate external vicinity - the outside space. Consequently, an out-
side space, the root to any building, is an integral part of its spatial pattern; at the
same time the relationship between any space inside a building with the root is a vital
factor in the syntactic analysis, particularly the computation of the shortest path.
In many of the examples published by the pioneers of space syntax (Hillier and
Hanson, 1984 & 1987) the outside node of a building is its front yard. As shown in
Figure 1, this node is not only one of the constituents of a building configuration, but
also one of its spaces, the front yard. Therefore, it is possible to connect any pair of
spaces, for instance space (c) and space (d) in Figure 1, inside a building through the
outside node, space (1). This type of relationship between an outside node of a house

partners presented their epistemology in articles in a variety of periodicals. For instance, Hillier and Leman (1973); Hillier
and Leman (1974); Hillier, Leman, Stansall, and Bedford (1976); Hanson and Hillier (1982).

Walker (1986) reviewed the "Social Logic of Space" and presented his views in an article that emphasizes some
similarities between the theoretical concept of the space syntax and other environment-behaviortheories.
T h e Space Syntax Methodology: Fits and Misfits 193

1 (the Front Yard)

Fig. 1. A Floor Plan of a Western European House (French) and its Permeability Graph; from Hillier
and Hanson (1987,370)

CY
13

FCY e 10
6

1 (the Street)
Key: 12 FWC, 20 MWC, 21 BAR

Key
8 Outside Node
Circulation
0 Function

Fig. 2. A Floor Plan of a Non-western House (Sudanese) and its Permeability Graphs

Note: For space abbreviations, see Appendix II.

walls that conceal the built form and courtyards of a house from the public domain.
Connectivity to the street is through gates positioned in the boundary walls, see
Figure 2. In such a situation, an outside node is a part of the spatial pattern but not
and its inner spaces is observed mainly in Western contexts. In other cultures, parti-
cularly Islamic and Middle-Eastern, where the open spaces, the courtyards, are part
of the functional areas of a house, an outside node of a building is always the street
or the public domain.3 In these cultures, houses are surrounded by boundary the

The relationship between the private space of a building, particularly housing, and the public domain differs with the
variation of culture (Rapoport, 1969 & 1977). In western cultures, single family houses--which provide suitable ground for
194 Khadiga M . Osman and Mamoun Suliman

building itself. Thus, it is inconceivable to consider a shortest path that connects two
spaces, say space (3) and space (6) in Figure 2, within the boundary of a building
through the street, space (1). This cultural variation in the conceptualization of the
outside node, hence the computation of the shortest path between any two nodes in a
setting, clearly shows the misfit of the space syntax concepts, as they exist, for the
analysis of non-Western buildings. To overcome such a misfit, a recursive4 compu-
ter program which is capable of performing the shortest path analysis, and hence the
other syntactic measurements as suggested both by the space syntax pioneers and by
this paper, is developed by the authors. In the added capacity of the program, the
shortest path between any two internal nodes in a network is computed with the ex-
clusion of any route that passes through the outside node. This feature, essential for
the analysis of the connected graphs of non-Western houses as explained before, is
not available in preexisting software packages which are specially designed to handle
space syntax procedures.
To illustrate the difference between the analytical approach of the space syntax (for
Western houses) and the modified computer program (for non-Western houses) sug-
gested in this paper, the example of a Sudanese house5 presented in Figure 2 is ana-
lyzed using both techniques. The data6 generated by applying the two programs is
given in Table 1 and Table 2. From Table 1, it is clear that the medium depth (md)
and integration (RA) values obtained by the two programs are different for some of
the nodes. For these nodes, the modified algorithm gives higher medium-depth
values and hence higher integration values than those of the Space Syntax. In other
words, the Space Syntax program reflects shallower and more integrated spaces rela-
tive to those indicated by the modified program.

comparison with compound houses of some Islamic societies--are normally surrounded by a front and/or back yard, a semi-
private transitional zone, that demarcates the boundary of a plot and relates the building to the neighboring private plots
and to the public domain, the street (Goffman, 1959; Cherayeff & Alexander, 1963). In non-western cultures, in particular
Islamic and middle-eastern, the built form of a house may be composed of several units that are connected to each other by
courtyard(s). Unlike in the west--where only a few domestic tasks take place beyond the roofed space--courtyards, in these
cultures, are part of the living quarters of the house and many domestic activities can be performed in the open air
(Rapoport, 1969). Thus, an outside node of this type of setting is not the front yard of the building, but the street or public
domain.

A computer program that has at least one procedure which calls itself many times in the execution phase

The Sudanese house example is extracted from a large sample collected by the author, K. M. Osman, in a field
research in 1991; for the results of this survey, see Osman (1993).

Since the two techniques result in two different sets of mean depth values, then only the syntactic paramelers
dependent on the shortest path values, particularly the RA and the RRA, are subject to change by the modified program.
The RA parameter is chosen here over the RRA for presentation and discussion because it can compare spaces within, and
not across, systems.
The Space Syntax Methodology: Fits and Misfits 195

Table 1
Space Syntax and the Modified Program Integration (RA) Values of a Sudanese House (Fig. 2)

row.
Table 2
Order of Spaces by Ascending (Lowest--Highest) lntegration (RA) Values

(i) Space Syntax Values


Node# 10 6 14 3 5 15 18 20 7 12 21
Space VerF FCY ChBR MCY Saloon FBR MBR FWC Kit MWC BAR
RA 0.153< 0 . 1 7 4 ~ 0.2051 0.222< 0 . 2 4 7 ~ 0 . 2 5 3 ~ 0.258= 0 . 2 5 8 ~ 0.274< 0 . 3 2 1 ~ 0.347

(ii) Modified Program Values


Node# 10 6 14 5 15 3 20 18 7 21 12
Space VerF FCY ChBR Saloon FBR MCY FWC MBR Kit BAR MWC
RA 0.153 c 0.189 < 0.205 c 0.253 = 0.253 < 0.258 = 0.258 = 0.258 < 0.289 < 0.347 < 0.353
/ Value

Note: For space abbreviations consult Appendix It.

The data obtained also detect a shift in the syntactic quality of some spaces as shown
by the results of the two techniques. For instance, according to the Space Syntax
results, the male courtyard (MCY) is more integrating than the saloon and the female
bedroom (FBR). The opposite is true in the data obtained by the modified program:
the saloon and the female bedroom are more integrated in the setting than the male
courtyard. Also, whereas the most segregated space by the Space Syntax values is
the bathroom (BAR), it is the male toilet (MWC) according to the modified program.
In reality, based on a personal observation of that particular house, the male toilet is
isolated from other spaces because of the limitation of its use, while the bathroom is
196 Khadiga M. Osman and Mamoun Suliman

positioned in such a way to serve both male and female domains.7 Generally, the
interpretation of the results of the modified program for Sudanese houses - the
example presented here being one of many -corresponds with the observed conclu-
sions, while that of the original program departs, in extreme cases, away from reality.
As a special case, it is fair to note that the two methods yield the same results for
single-gate houses, western or not, since the outside node has no influence what-
soever in the calculation of the shortest path between nodes inside.

4.2. The inherent binary coding


One of the problems associated with the application of the space syntax and graph
theory in general stems from the fact that these methods use a binary coding, of zero
and one, to express the link between a pair of spaces for the purpose of drawing
graphs and generating the quantitative measurements associated with the method.
Such an approach equates all types of connectivity which may exist between adjacent
spaces; also those between non-adjacent spaces - spaces linked to each other
through a third common space. Specifically, the space syntax method perceives
connectivity through doors as equivalent to connectivity through archways, and
equates short corridors that link two non-adjacent spaces with lengthy ones in a sirni-
lar position. For instance, in Figure 3, it is clear by observation that the correspon-
ding nodal diagrams of plans (a-c) are alike; hence, as shown in Table 3, all the syn-
tactic properties of these plans are the same. Similarly, Figure 4 (a-c) and Table 4
show identical graphs and similar sets of RA values for all three plans, respectively,
regardless of the variation of the size and shape of space (4) in all of them. In reality,
the spatial and visual continuity between two adjacent and non-adjacent spaces
depends on two variables: i) the type of plane - continuous, discontinuous, frees-
tanding, portable, etc. - and ii) the nature of the space - a long or short corridor,
dominant, equivalent, etc. - that connects or separates between two spaces (Chang,
1979).
The application of the space syntax method is particularly difficult in modern open
floor plans where the boundaries between spaces are set by function and furniture
rather than by physical barriers, and in compound-type dwellings where courtyards
are constituent parts of the living space. In such situations, before drawing the
graphs associated with each floor plan, a researcher has to weigh hard and subjective
options in order to divide an open roofed or unroofed space into its constituent
convex spaces, as shown in Figure 5, prior to drawing permeability graphs and quan-
tifying the syntactic parameters. The connectivity between such artificially broken
spaces, which are actually one unit, is regarded by the method as equivalent to the
connectivity between spaces which are physically separated. For example, in Figure
5 the connectivity between space (18) and space (20), both in fact represent one unit,

As described by Karrar (1981) and Lee (1977), the traditional Sudanese house is generally divided into two domains.
The front, the least sacred part, is exclusively for men. The back and the most secluded part of the house is for women.
The Space Syntax Methodology: Fits and Misfits 197

is assumed equivalent to the connectivity between space (18) and space (19) which
are separated by a physical barrier.

a) a Door in a Continuous Plane;


b) Two Openings in a Free Standing Plane;
c) a Discontinuous Plane
Fig.3. Three Examples IllustratingSome of the Types of Connectivity that may Exist Between Two
Adjacent Spaces.

Table 3
Integration (RA) Values for Plans (a-c) of Figure 3

Thus, these analytical procedures result in misleading interpretations since they do


not induce values that reflect the actual building fabric. Consequently, coming up
with adjusted connectivity values generated by a fuzzy, rather than a binary, coding
system that would consider all type of connections existing between a pair of spaces,
and the development of a computer program that performs all the corresponding syn-
tactic functions - on a fuzzy logic base - is of significant importance for the
upgrading and the development of the space syntax method and hence for future
research in the field.
198 Khadiga M. Osman and Mamoun Suliman

(c)
a) Short Corridor; b) Long Corridor; c) a Third Functional Space

Fig. 4. Three Examples Illustrating Some of the Types of Connectivity that may Exist Between Two
Non-Adjacent Spaces.

Table 4
Integration (RA) Values for Plans (a-c) of Figure 4

4.3. The intotality of the cultural interpretation of the measurements


The approach of the morphological interpretation of buildings provides a systematic
method of analysis. Using the space syntax, diverse types of buildings may be des-
cribed and compared by projecting their underlying configuration and interpreting
their syntactic properties, i.e. property of depth, integration, control, and connecti-
vity. However, as Lawrence (1990: 75) writes "the mere act of transforming the two
dimensional representation of a building from a traditional scale drawing to a graph
does not yield any information about psychological, social, cultural, or temporal
issues."
Furthermore, the meaning and use of space as well as the interaction among the users
are not solely dependant on the building form (Rapoport, 1969 and Lawrence, 1990).
T h e Space Syntax Methodology: Fits and Misfits 199

Thus, to pursue the study of cultural context of buildings by the mere analysis of its
configuration, is quite unreasonable.

I
(a)Floor Plan (b)Convex Map

Fig. 5. An Example of a Compound Type Dwelling.

The space syntax method intends to deduce formal physical properties of buildings
that inhibit or encourage personal contacts among the user - individuals or social
groups - as dictated by their culture. According to the syntactic interpretations of
the method, low integration values mean segregation and privacy, while high inte-
gration means high connectivity and less privacy. To rely totally on such analysis
and to accept their interpretations, means to agree that the degree of physical seg-
mentation and division of space in buildings is an indication of the social and cultural
norms that govern the relationships among the user. This may be true to a certain
extent, but, as explained below, a growing number of studies has shown that the
degree of segmentation and division of building space is not indicative of the degree
of the interface among the inhabitants.8
For illustration, some cultural groups - the Berber of north Africa (Bourdieu, 1973,
1977), the Bari of the Amazon forest (Jaulin, 1971), the Betsilo of Madagascar (Kus
& Raharijaona, 1990) among others - inhabit dwellings which have no internal
physical division, i.e. the whole living space is one open unit. If we apply the space
syntax method, the graphical representation of such homes, as shown by Figures 6-7,
are all composed of two nodes - one is the outside node and the other represents the
internal built form. Following the space syntax interpretations, it is easy to conclude

Gans (1968) in his famous book "People and Plans," drew the attention to the difference between the induced,
"potential," use of the built environment implied by the design and the actual, "effective," use dictated by the norms of
inhabitants.
200 Khadiga M. Osman and Mamoun Suliman

that the cultural norms that govern the interaction among the members of each of
these three groups are similar since the houses of the three groups have the same
morphology. However, the ethnographic analysis of Bourdieu (1973 and 1977),
Jaulin (1971), and Kus and Raharijaona (1990) reveal that each of these cultural
groups has a distinct set of rules which is used to divide the internal space and regu-
late the relationship among its members. As a result, to avoid such misleading inter-
pretations, the space syntax approach must be supplemented by the analysis of all the
variables - social, cultural, and others - implicated in the production of the built
environment.
In a study of Sudanese houses (Osman 1993), the modified procedure of the spaces
syntax, mentioned earlier, coupled with socio-demographic analysis,g proved to be
indispensable for eliciting cultural variables behind spatial settings. The results
obtained by the application of one method of analysis complement and hence solidify
those obtained by the other. For instance, the ethnographic study reveals the gender
division in the conduct of activities and the use of space, whereas the spatial analysis
highlight the morphological pattern of segregation in the Sudanese house. In other
words, the two methods, in combination, indicate that the traditional Sudanese house
not only is divided into malelfemale quarters, but also that these quarters are spatially
segregated. Such comprehensive findings cannot be reached if only one of these two
methods, the modified space syntax and the ethnographic research, is employed.
sleeping mat utensils
storage

window

House inner
space

utensil storage
water jar Outer space
door

chicken coop
and cooking area
storage area

Fig. 6. A Floor Plan of a One Room Betsileo House and its Respective Permeability Graph; from
Kus (1 990, 25)

This approach is based on a concurrent investigation of both spatial and aspatial features of housing (Osman, 1993).
It is in line with the arguments presented by Foley (1964), Barker ( 1 9 6 0 and Rapoport (1980; 1989 & 1990).
The Space Syntax Methodology: Fits and Misfits 201

Stable

House inner
space

west door
(femalef
Outer space

Fig. 7. A Floor Plan of a Kabylie Berber House and its Permeability Graph; from Oliver (1971, 162)

5. Conclusion
Around a decade since space syntax was first published, it still remains a controver-
sial technique. Many of its critics, few of them architects, have questioned the vali-
dity of the method in interpreting the social norms of inhabitants. They claim that
the existing analytical procedure falls short of fulfilling the complex goals set by the
pioneers.
This paper goes an extra step beyond the published criticism to outline the fits and
misfits of the technique and to propose some solutions. It argues, with illustrations,
that regardless of the advantages of the space syntax, there are limitations to the
method which hamper its findings and, subsequently, their interpretation. First, the
possibility of including the outside node in the shortest path calculation for any
internal pair of nodes does not fit non-Western houses where the outside node repre-
sents the public domain. Hence, a modified approach for the calculation of the
shortest path is proposed. Second, the analytical procedure, as it exists, does not
generate data that describe built-forms as seen in reality because of the limitation of
the binary coding. To project reality, weighted or fuzzy connectivity, instead of
binary, has to be considered. Third, the space syntax methodology alone is incapable
of eliciting the cultural norms of societies governing the use of building. It should be
supplemented by social science methods; they are much more equipped for such a
purpose.
202 Khadiga M. Osman and Mamoun Suliman

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Appendices

Appendix I

Space Syntax Selected Mathematical Formulae


Mean depth (md) = I/ (K - 1 ) . I:(all depth values between a point & all other points in a graph) (1)
The depth value between two points in a graph is equal to the minimum number of connections that must be
taken to reach from one point to the other (the shortest path).
K is the total number of nodes in a graph, including the outside node.
Relative Asymmetry (RA) = 2 (md - 1)/ (K - 2) (2)
Real Relative Asymmetry (RRA) = RA/ X (3)
where - 3K + 2)
X = [ 6.644K. loglo(K + 2) - 5.17K + 2 ] / ( K ~
Control Value = lNal(b) (4)
D(a,b)=l
where D(a,b) represents the connectivity (shortest path) between points (a & b), and Val(b) is the number of
direct connections for point (b). So the control value for any point (a) is calculated by summing the reciprocal
of the number of connections for each point directly connected to (a).
Note: For further elaboration on these measurements and others, consult Hillier (1984 & 1987) and Peponis
(1985).
Appendix II

Space Abbreviations

Abbreviation Meaning
BAR Bathroom
ChBR Children Bedroom
CY Courtyard
DBR Dependant Bedroom
FBR Female Bedroom
FCY Female Courtyard
WC Female Toilet
Kit Kitchen
MBR Master Bedroom
MCY Male Courtyard
MWC Male Toilet
Ver Veranda
VerF Female Veranda

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