16

SPACE SYNTAX METHODOLOGY

Ulrich Thaler

Introduction
You may not have heard of Harry Beck (Garfield, 2012, pp. 291–296), but he has probably made your life
easier at one time or another (though nobody asked him to). Beck was working as a technical draughts-
man for the London Underground Signals Office when, in 1931, he submitted a radical new draft, pre-
pared in his spare time, for the London Tube map, which had been inspired by electrical diagrams and
the realization that, once on an Underground train, passengers did not care overly much about physical
distance. You will recognize Beck’s diagram (Figure 16.1(b)) immediately, because this is, in principle,
the Tube map still used today, a design icon printed on tourist mugs and emulated by local transport
authorities worldwide. Although schematic single line diagrams had appeared as early as 1909, the pre-
Beck map of the entire network was still drawn and often also shown superimposed over a road map
of the city (Figure 16.1(a)). What Beck had done, in effect, was to transform a geographical map into
a topological one, forgoing metric properties for relative relationships and thus producing a simplified
model of the system which still retains the properties essential to its users. This, in a nutshell, is what space
syntax methodology (Al Sayed, Turner, Hillier, Iida, & Penn, 2014; Hanson, 1998; Hillier, 1996; Hillier &
Hanson, 1984) aims to do as a statistical topological or network analysis of built contexts at the settlement
or building level, as explained below.
Before looking into details of methodology, however, we should take a brief look at the history of
space syntax and, perhaps, the distinction between space syntax theory and space syntax methodology.
Space syntax was formulated as an approach to the configurational analysis of built contexts at University
College London’s Bartlett School of Architecture from the mid to late 1970s on by a group of researchers
around Bill Hillier and, later, Julienne Hanson. As results from space syntax analyses, of integration in
particular, and real-word observations of movement and traffic flows showed good correlations and due
to its resulting ability to model the global effects and repercussions of local changes within a given spatial
configuration (cf. Hillier, Penn, Hanson, Grajewski, & Xu, 1993), space syntax quickly gained traction as a
predictive tool for architectural and urban planning, fostering an extensive research community. Although
it never became part of archaeology’s methodological mainstream (if such a thing exists), most likely due
to the high quality and density of data it demands, space syntax was also picked up by some archaeologists
(e.g. Gilchrist, 1988; Foster, 1989) with surprising alacrity given the discipline’s usual tendency to adopt
more seasoned approaches from other fields. Indeed, even an early emphatic criticism (Leach, 1978) of
FIGURE 16.1 London Tube maps: (a) the 1908 version superimposed on a city plan. (b) the 1933 version featur-
ing H. Beck’s topological redesign.
Source: Figures 16.1(a–b): © TfL from the London Transport Museum collection (ref. nos. 2002/264, 1999/321)
298 Ulrich Thaler

space syntax in an archaeological volume (though formulated by a social anthropologist) predated by six
years the publication, in 1984, of the volume familiarly known as the ‘Old Testament’ in the space syntax
community, Hillier’s and Hanson’s “The social logic of space” (Hillier & Hanson, 1984).
It should also be noted that the analytical techniques we are concerned with here, then labelled
“alpha analysis” and “gamma analysis” for settlement and building level analyses respectively (Hillier &
Hanson, 1984, pp. 90–123, 147–155), were only introduced as one part of a wider intellectual agenda
in “The social logic of space”, a book that drew widely on ethnographic examples and sought to arrive
at fairly broad generalizations on its title matter. Another strong focus besides analytical techniques
was on considerations of how seemingly complex settlements as ‘global’ structures could arise from
specific, but potentially simple ‘local’ rules. Indeed, such “generative syntaxes” appear to have been the
first topic of discussion in the development of space syntax (Hillier, Leaman, Stansall, & Bedford, 1976),
which thus started out from a perspective that can be broadly termed as structuralist. Nonetheless, at
least some degree of appreciation of the recursive relationship of social (acts) and built structures can be
found in “The social logic”, and by the time Hanson and Hillier published their next major volumes on
urban/settlement and architectural/building studies respectively, “Space is the machine” (Hillier, 1996)
and “Decoding homes and houses” (Hanson, 1998), their stance can certainly be characterized as post-
structuralist. This shift, perhaps, might serve as an indication that the analytical techniques developed
under the label of ‘space syntax’ are actually compatible with different theoretical perspectives and frame-
works. Efforts (or at least calls) to align space syntax with a phenomenological perspective (Seamon, 1994,
2003) may provide a particular interesting illustration of this point for the archaeologist, who is elsewhere
reminded that phenomenological approaches do “not translate well into a formal theory, nor a fixed set
of methodological techniques” (Tilley, 2005, p. 202). Indeed, the continued advocacy of space syntax
as an encompassing theoretical framework by Hillier in particular (e.g. Hillier, 1999a, p. 165, 2008; cf.
Batty, 2004, p. 3) seems to contrast somewhat, at least from the etic perspective of an archaeologist, with
a mainstream within the space syntax community that is strongly oriented towards practical applications
in architecture and urban planning. Emicly speaking, it is certainly true that in archaeology itself, as well
as related disciplines such as social anthropology (cf. Dafinger, 2010, pp. 125–127, 134–140), space syn-
tax’s broader theoretical aspirations have mostly been ignored in favour of a pragmatic approach which
conceives of space syntax as a methodological tool. Notwithstanding the inspiration that may be found
in the more abstract considerations presented by Hillier, Hanson and others, the present text is therefore
deliberately framed as an introduction into “space syntax methodology”.

Method

Basic principles
Let us begin with a concrete historical example, the ground floor plan (Figure 16.2(a)) of a 17th century
residence of minor German nobles, Schloss Friedeburg in Saxony-Anhalt (Schwarzberg, 2002). In the
terms of network analysis, each room can be understood as a node and each (inside) door as an edge
connecting two nodes. For a corresponding visual representation, we can inscribe a dot in each room and
link these with straight lines where a door connects two rooms and thus arrive at a topological graph (Fig-
ure 16.2(b)). Since the information content of this graph no longer depends on the nodes’/dots’ relative
position to one another – the relevant relationships are shown by the lines representing the edges – this
graph can then be rearranged. The most commonly used form is the so-called justified graph (Al Sayed
et al., 2014, pp. 13–14; Hillier & Hanson, 1984, pp. 106–108, 149), or j-graph for short (Figure 16.2(c)).
In this, the outside of the building, referred to as the carrier space, is shown as a further node at the root
 Space syntax methodology 299

FIGURE 16.2 Schloss Friedeburg, Saxony-Anhalt, Germany. The ground floor of the main residential building
(17th c. CE): (a) the state plan of 1930. (b) a simplified plan with points of access marked by arrows, topological
graph superimposed. (c) the justified graph with room types, rings and depth from carrier indicated. (d) the
path matrix with sums of path lengths.
Source: Figure 16.2(a); Schwarzberg (2002), Figure 1

of a dendritic graph in which nodes are arranged in horizontal lines according to their distance from the
outside, i.e. the minimum number of doors/edges through which they can be accessed.
The j-graph already permits the determination of some numerical indicators of specific spatial prop-
erties. Ease of access from the outside as a quality of a given room or an entire building, for example, is
reflected in its depth or mean depth as numerical indicators.1 In the graph, the depth of each node can
easily be determined by simply numbering the horizontal lines of nodes (for the simple reason that this
is how the graph is organized in the first place), which in turn allows us to calculate the mean depth, a
first important indicator of how accessible the building as a whole is from its surroundings. As to internal
structure and relationships, the number of rings identifiable in the j-graph (and thus the system) offers
a first indicator of route choice options, while each individual room/node can be characterized by, on
the one hand, its connectivity, i.e. the number of immediate links with other nodes, and as an a-, b-,
c- or d-type space (Al Sayed et al., 2014, p. 14; Hanson, 1998, pp. 173–174; Hillier, 1996, pp. 318–320;
Figure 16.2(c)). Spaces of type a display a single edge, i.e. are ‘dead-end’ rooms accessible through but
one door and thus strongly controlled by other spaces. In contrast to the a-type tips of the branches in
a dendritic system, b-type spaces constitute the (stems of) the branches themselves, i.e. they are at least
and indeed most typically two-edged – both literally and figuratively – in that they offer some degree of
control, as least locally, but contribute only moderately to linking up a system in global terms. The latter
300 Ulrich Thaler

is more characteristic of c-type spaces, i.e. those two- or more-edged nodes which form part of a (or
more precisely: one single) ring, and d-type spaces, which form part and thus link two or more rings and
consequently are the main connectors within a building (if, indeed, the configuration contains d-type
spaces at all).
While this categorization permits a first idea of the ‘connectedness’ – a local quality – and furthermore
the ‘centrality’ of a space within the network of spaces – a global quality of (literally) central importance
in space syntax analyses and referred to as integration – a better idea of the latter is gained if we do some
sums. The easiest way to do so (without a computer), but one rarely explicitly discussed (somewhat
surprisingly, unless you consider the ubiquity of computers), is a path matrix (Figure 16.2(d)) in which
the path length or step distance, i.e. the number of edges traversed, between each pair of nodes is noted
(Blanton, 1994, pp. 34–35). This permits the calculation of a sum of path lengths for each space/room.
The most integrated room in a building, i.e. the one most easily reached from all others, will be charac-
terized by the lowest, the least integrated by the highest sum of path lengths. From the sums we can also
calculate the mean path length (or mean distance, MD) for every space and from this and the number of
spaces (k) in a given system, Hillier and Hanson derived a numerical indicator of integration which they
termed ‘relative asymmetry’:

2 × ( MD − 1)
RA =
k−2
As the terminology indicates, this measure was intended to compare “how deep the system is from
a particular point with how deep or shallow it theoretically could be” (Hillier & Hanson, 1984, p. 108)
and express this in values from 0 to 1; the word ‘asymmetry’ denotes the non-correspondence of actual
and theoretically possible depth. Higher asymmetry, however, means lesser integration of a space, so that,
somewhat counter-intuitively, relative asymmetry as an indicator of integration – i.e. the spatial quality
we are, after all interested in – gives higher values for less integrated and lower values for better-integrated
spatial units. The crucial advance over simply doing sums, on the other hand, is captured in the word
‘relative’: asymmetry and integration are now considered in relation to the size of the system, i.e. relative
asymmetry takes into account how big a building any given room is in.
If instead of a single room, we look at and want to characterise the building in its entirety, not only
can we calculate mean values for depth, relative asymmetry and (as we will see) other numerical indica-
tors, but we can also consider its ‘core’ and ‘genotype’. The integration core is defined as the subset of
the (typically 10%) most highly integrated spaces (Al Sayed et al., 2014, p. 15; Hillier & Hanson, 1984,
p. 115); it may be of interest, e.g., in how far the core penetrates certain sections of a larger building or
bypasses others. The notion of a topological genotype (Hillier & Hanson, 1984, pp. 143–175; Hillier,
Hanson, & Graham, 1987), by contrast, does not aim at a more detailed internal description of a layout,
but a simplified one for comparison with other contexts. If specific room functions are attested across a
sample of buildings in a consistent hierarchy of integration – e.g. kitchen > (read: more highly integrated
than) reception room(s) > work space(s) > bedroom(s) – then this re-current organizational scheme,
which may be obscured by very different ‘phenotypical’ built forms, is referred to as a building genotype,
which can be characteristic, e.g. of certain building functions and/or cultural or social contexts.
Comparison between buildings, however, also leads us to a crucial methodological difficulty: while
relative asymmetry as a standardised value is easier to work with than sums of path lengths and while
one might thus expect it to facilitate reliable comparisons between different buildings and, in particular,
buildings of different sizes with accordingly very different sums of path lengths, the latter, unfortunately,
is not actually the case; we will address this issue later.
 Space syntax methodology 301

Nodes and edges

For now, there are two directions in particular in which we can and need to expand on the first principles
set out above. While we will later take a look at different spatial properties and their numerical indicators,
the first vector of expansion concerns the nodes and edges which constitute the configurational frame-
work. So far, we have spoken of the rooms of a building as nodes and the doors between them as the cor-
responding edges. But although rooms may constitute the most intuitive set of nodes for configurational
network analysis, any set of consistently defined spatial entities or units which are meaningfully linked to
one another by corresponding edges can be subjected to the same kind of analysis (Hanson, 1998, p. 270;
Hillier, 1999b, p. 169). Indeed, rather than with the ‘rooms’ of everyday parlance, space syntax analyses
more typically are concerned with ‘convex spaces’ (Al Sayed et al., 2014, p. 12; Hillier & Hanson, 1984,
pp. 97–98). A convex space is defined as an area whose perimeter is not intersected by the connecting line
of any pair of points within it or, differently put, within which any two points are directly intervisible.
Edges are then defined by adjacency; this is not, nota bene, the adjacency of rooms sharing a door-less
wall, but the congruence of part of the perimeter of two spaces. Happily, in most architectural contexts
at the level of the individual building (rather than the context of an entire settlement), the differentiation
between rooms and convex spaces is largely a notional one in principle and a matter of resolution in
practice (Figure 16.3(a)):2 any recessed window or projecting half-column will, strictly speaking, break up
a given room into two or more convex spaces, but not any minor deviation from a basically rectangular
(and thus convex) shape need be included in a meaningfully analysable ground plan.
The formally defined convex break-up, i.e. the set of “fewest and fattest” convex spaces that cover
the entire accessible area within a built context is, however, fundamental for the definition of a second
set of nodes and edges, referred to as the axial break-up or axial map (Al Sayed et al., 2014, pp. 11–12;
Hillier & Hanson, 1984, pp. 99–100). This comprises the smallest set of longest lines of sight that cov-
ers, i.e. reaches, all convex spaces in a given spatial layout and additionally replicates all rings within it
(Figure 16.3(b)). When axial lines are taken as nodes of a network, their intersections will form the edges
(Figure 16.3(d)); once the axial break-up is mapped in this manner, a j-graph (Figure 16.3(f)), path matrix
and numerical indicators of spatial properties can be derived from it in the same way set out above for
rooms (/convex spaces). Early on, a connection was proposed between “axiality [and] movement into
and through the system” as well as between “convexity [and the system’s] organisation from the point of
view of those who are already statically present in the system” (Hillier & Hanson, 1984, p. 96; cf. Al Sayed
et al., 2014, p. 15). In practice, although both perspectives can offer meaningful results at both levels,
convex analysis has found broader application in analyses at the building level, whereas axial analysis has
developed into a mainstay of analyses at the settlement level. It is therefore perhaps not surprising, given
the strong focus on urban planning within the wider space syntax community, that axial analysis has seen
a number of further developments.
These include, most notably, the line segment break-up and the weighting of nodes and, more typically,
edges; both developments are combined in segment angular analysis (Al Sayed et al., 2014, pp. 71–98,
116–117; Dalton, 2001; Hillier & Iida, 2005; Turner, 2000, 2001a; cf. Stöger, 2011, pp. 63–64, 215–219, as
an example of the still rare implementation in archaeology). The line segment break-up is based on (and
as a visual representation congruent with) the axial map, but the unit of analysis, i.e. the node, is no longer
defined as the entirety of an axial line but rather as the line segment between two intersections of axial
lines (or one such intersection and the end of an axial line; Figure 16.3(b)). In principle, edges could then,
as in convex analysis, be defined in terms of adjacency; but in fact, angular analysis diverges from ‘classical
space syntax’ in that it no longer uses a binary concept of an absent or present connection between two
spatial units, nor consequently step distance (i.e. fewest turns in the conventional axial map) as a measure
302 Ulrich Thaler

FIGURE 16.3 (a–c) Simplified ground floor plan of the main residential building of Schloss Friedeburg: (a) with
the non-convex rooms highlighted and a suggestion for (approximately convex) subdivision of non-convex
rooms 1 and 6. (b) with the axial map superimposed and line segments indicated for the longest and most
integrated axial line. (c) with three overlapping isovists and their centre-points indicated. (d) the axial map of
the ground floor of the main residential building of Schloss Friedeburg, with the topological graph of axial
break-up superimposed. (e) examples of diamond-shaped topological graphs. (f) justified graph of the axial
break-up of the ground floor of the main residential building of Schloss Friedeburg.
Source: Figures 16.2(b–d), 16.3–16.4: by the author

of distance between two spatial entities. Instead, the distance between two spatial units is given as the least
sum of angles that need to be turned on a connecting path. Thus, geometrical properties of the spatial
layout under study are reintroduced into the formerly purely topological analysis.
In a similar though perhaps less direct way, the realm of ‘topology simple and pure’ is transcended when
isovists are taken as the nodes in a network analysis, with the isovists’ overlaps establishing the edges of
the network graph (Al Sayed et al., 2014, pp. 27–38; Turner, Doxa, O’Sullivan, & Penn, 2001; Turner &
Penn, 1999). The isovist (Benedikt, 1979) is defined as the volume or, in the present context, area of space
visible from a given point (Figure 16.3(c)); essentially this is what in geographical terms would be called
a viewshed (see Gillings & Wheatley, this volume). In contrast to the number of convex spaces or the
 Space syntax methodology 303

minimum number of axial lines in a given spatial layout, the number of points – each of which allows the
construction of an isovist – within that layout is, of course, infinite. Hence, Visual Graph Analysis (VGA)
starts by superimposing an arbitrary grid over a layout and then constructing isovists of the centre points
of the raster cells. From this point on, analysis again follows the established methodology of ‘classical space
syntax’, yet at least two marked differences between VGA and convex or axial analysis deserve mention.
The first lies in the fact, already alluded to, that the regular grid brings with it a notable degree of sen-
sitivity for metric properties; the metric size of a given room within a building will influence the visual
integration of the points within it (which are, after all, normally intervisible). The second concerns the
way we use the results of VGA; as the centre point of a raster cell is not an intuitively meaningful spatial
entity in the same way as a visual line or – a fortiori and even under the designation ‘convex space’ – a
room are, the interpretation of results from VGA will typically focus less on numerical indicators for
individual spatial units and more on the ‘heat map’ of integration as, perhaps aptly, a visual representation,
in which red/light denotes highly and blue/dark weakly integrated areas. This does not diminish VGA’s
potential for study both at the building and the settlement level.

Qualities and indicators

Having looked at edges and nodes, we will now turn to spatial qualities and their numerical indicators,
starting with the problem left open earlier: if we are to compare integration as a configurational quality
between different built contexts of different sizes or individual rooms within them, then the numerical
indicators we use to describe this quality need to be robust with regard to differences in size between the
contexts under comparison. Yet, in reality, spatial configurations themselves display some sensitivity to
size. Linear topological arrangements such as a single string of b-type rooms ending in an a-type space
offer a simple, but telling illustration: a three-room structure following this configurational principle will
provide a habitable building or part thereof. But a 13- or even 43-room building configured in accor-
dance with the same principle, i.e. without c- and d-type spaces or even branching, would be eminently
impractical (at least for most purposes). So, for any meaningful comparison between different contexts,
numerical indicators have to be calculated in a way that corrects for the size-sensitivity of configurations,
a process referred to as ‘normalisation’.
For this reason, Hillier and Hanson quickly followed their theoretically derived relative asymmetry
(RA; see earlier) with a second, empirically adjusted numerical indicator of integration termed ‘real rela-
tive asymmetry’ (RRA; Hillier & Hanson, 1984, pp. 109–113). The underlying idea is simple: In a first
step, RA values are calculated for a standard set of j-graphs of different sizes but of the same basic shape
and organizational structure (Figure 16.3(e)), i.e. of systems that should ‘behave’ similarly irrespective of
their size. These RA values, designated as ‘D-values’ in reference to the diamond shape of the underlying
j-graph series, can be compiled in a reference table and then used as correction factors for values from
real-life contexts. This means that RRA for a spatial unit in a system of a given size k is calculated by
dividing the unit’s RA by the D-value corresponding to the system’s size:
RA
RRA =
Dk
In practice, there happily is no need to regularly consult a reference table, as D-values for differently-
sized systems can also be calculated by a logarithmic formula:

   k + 2   
2 × k ×  log 2  − 1 + 1
   3   
Dk = 
(k − 1)×(k − 2)
304 Ulrich Thaler

Inserting this formula for Dk as well as that for RA in the calculation of RRA, we arrive at:

RA  2 ×(MD − 1) ×(k − 1)×(k − 2)

RRA = =  
Dk     k + 2   
2 × k ×  log  
   2  3  − 1 + 1×(k − 2)
    
With RRA, we have arrived at a numerical indictor for integration that has proven robust in practi-
cal application with regard to size-sensitivity. As, however, its calculation no longer produced values in a
standardized range, as RA, while retaining RA’s counterintuitive trait of giving high values for low and
low ones for high integration, RRA eventually came to be replaced by an indicator simply termed, as the
quality it described, ‘integration’ (I; Al Sayed et al., 2014, pp. 15, 114) and calculated, equally simply, as
the reciprocal of RRA:

   
2 × k ×  log  k + 2  − 1 + 1×(k − 2)
  
1
  
  
2 
 3  
 
I HH = =
RRA  2 ×(MD − 1) ×(k − 1)×(k − 2)
 

If this seems like a less than perfectly elegant way of arriving at a crucial measure, we should not be
surprised by criticism or efforts at improvement. For axial analysis, these include, e.g. the proposals of an
alternative series of gridded rather than diamond-shaped standard j-graphs for the production of correc-
tion factors (Kruger, 1989), and even of an alternative calculation of integration based not on the prob-
lematic RA, but directly on the sum of path lengths (Teklenburg, Timmermans, & van Wagenberg, 1993):

 k − 2 
ln 
 2 
I Tekl =
ln (∑ D − k + 1)

Similarly, in the context of VGA, both the revival of P-values (de Arruda Campos & Fong, 2003),
developed by Hillier and Hanson (1984, pp. 113–114, cf. pp. 73, 95) as an alternative to D-values in a
very specific form of analysis of building-to-settlement relationships, but never widely used, and, more
radically, the abandonment of standardized integration measures in favour of simple mean path lengths
(Sailer, 2010, pp. 132–133) have been suggested. To the best of my knowledge, however, such proposed
alternatives seem to have been mostly ignored rather than refuted (let alone accepted and adopted),
leaving the calculation of I a black box that a thriving research community mostly seems loath to open.
Recent discussions of normalisation in the context of angular analysis need to be noted as an exception
(Al Sayed et al., 2014, pp. 77–78, 117; Hillier, Yang, & Turner, 2012), but the results are not transferable
to other types of analysis.
This might encourage us to look at other spatial qualities and their numerical indicators within space
syntax, of which there are a number. We have already encountered, in the introductory section, con-
nectivity as a simple local measure, i.e. the number of other nodes with which a given node shares edges.
Control is another local measure, calculated by assigning, for each space, the reciprocal of its connectiv-
ity to each of its neighbours and then summing up the apportioned values for each space; it is taken to
capture the degree to which a space controls access from other parts of the network to its immediate
neighbours (Hillier & Hanson, 1984, p. 109). The correlation of connectivity and integration (which,
 Space syntax methodology 305

of course, cannot escape potential problems with the latter) is referred to as intelligibility and taken to
describe how far the global connective role of a spatial unit can be inferred from within that space (Al
Sayed et al., 2014, p. 15; Conroy, 2000, pp. 61–88; Hillier, 1996, p. 120).3
Despite their more specific uses, however, none of these measures comes close to integration in
either its apparent predictive potential or in its popularity among researchers, whereas a more seri-
ous ‘contender’ or complement to integration has come to the fore in recent years for some types of
analysis: choice (Al Sayed et al., 2014, pp. 15, 77, 114–115, 117; Freeman, 1977; Hillier & Iida, 2005,
p. 483; Turner, 2007). Like integration, choice is defined in reference to the set of shortest paths
between any pair of nodes within a system. But in contrast to the integration value of a given space,
which takes into account the shortest routes from that space to all others (which are the same as those
from all others to this particular space), its choice value reflects how many shortest routes between
pairs of other nodes pass through the space under consideration; fittingly, ‘betweenness’ has been used
as an alternative designation (Al Sayed et al., 2014, pp. 114, 117; Turner, 2007, p. 540). Consequently,
choice has been advocated as an indicator of the “through-movement potential” (Al Sayed et al.,
2014, pp. 26, 73; Hillier, 2007/2008, p. 2) of a node, i.e. its likeliness of attracting passing traffic, by
contrast with integration which is held to capture a node’s “destination potential” (Hillier, 2007/2008,
p. 2) or “to-movement potential” (Al Sayed et al., 2014, p. 73), i.e. its likeliness to attract visitors or
simply its accessibility. This reflects, to some degree, the earlier opposition of axial space as connected
with movement and convex space as linked to static activity. It is therefore perhaps not surprising that
choice, considered “descriptive of movement rather than occupation” (Al Sayed et al., 2014, p. 15), is
not usually used in convex analysis, despite the popularity it has gained in forms of axial analysis and
in the context of line segment analysis in particular.
A last methodological aspect that we need to address concerns the contrast between local indicators,
such as connectivity and control, and global indicators, like integration and choice: while the latter make
reference to a space’s relationship with all other spaces within a given layout, the former take into account
only the relationships of a space to its immediate neighbours. There is a third possibility, which is consid-
ering a space’s relationship to all those which fall within a certain radius around it (Al Sayed et al., 2014,
pp. 15, 25, 114; Hillier, 1996, pp. 99–101). A space’s integration in the context of all those spaces within
three topological steps from it, e.g. is referred to as integration at r = 3 or, with a more general term that
can refer to other small radii as well, as local integration (global integration, in this sense, is at r = n, while
local indicators in the strict sense are established at r = 1). While calculating integration locally offers a
useful supplement to global integration values in, e.g. a convex break-up where it can help to establish
independent hubs of circulation, in studies of angular choice the analysis of different metric rather than
topological radii takes on even greater significance in that it promises, at least in present-day contexts,
a means of distinguishing between factors influencing vehicular and pedestrian traffic flows (Al Sayed
et al., 2014, pp. 25, 74). How readily the latter can be transposed into different archaeological contexts
may be debatable, but an example for the usefulness of local convex integration will be given in the fol-
lowing case study.

Case study
The Late Bronze Age palace of Pylos in Western Messenia (Blegen & Rawson, 1966), one of the early
state centres of Mycenaean Greece, offers very favourable conditions for space syntax analysis in two
regards in particular: First, a careful study of changes to the building over the course of the 13th century
BC allows us to distinguish – and then analytically compare – an earlier and a later state of the building
(Nelson, 2017, pp. 360–365 Figures 4.7–4.8; Thaler, 2018, pp. 39–59; Wright, 1984; Figure 16.4(a–b)).4
FIGURE 16.4 The Palace of Pylos (Ano Englianos), Messenia, Greece (13th c. BCE): (a) a simplified plan of the
earlier building state with results of VGA and the shortest convex routes to throne room 6 superimposed as a
partial topological graph. (b) a simplified plan of the later building state with results of VGA and the shortest
convex routes to throne room 6 superimposed as a partial topological graph. (c) a simplified plan of the later
building state with shading indicating areas of convex spaces most easily accessible from the three different
points of access (indicated by arrows) and separate j-graphs for access through each of the latter (grey indicating
the spaces of the service ‘wing’). (d) a simplified plan of the later building state with shading indicating areas
of convex spaces most easily accessible from the three main courts 58, 63 and 88, “A” marking the archive,
“NEB” the Northeastern Building (the presumed clearing-house) and “P” pantries (courts assumed to be
served from these are indicated by subscript nos.). (e) j-graph of the later building state (grey indicating the
spaces of the service ‘wing’).
Sources: Figures 16.2(b–d),16.3,16.4: by the author
 Space syntax methodology 307

Second, a more impressionistic comparison of those building states has already been crucial in formulat-
ing a hypothesis that dominated our understanding of the Pylian palace complex for over two decades, i.e.
the assumption that its architectural development reflected a long-term economic decline (Shelmerdine,
1987; Wright, 1984), in reaction to which, among other things, “changes to the palace [. . .] consistently
[. . .] restrict[ed] access and circulation” (Shelmerdine, 1987, p. 564); sometimes this has even been associ-
ated with defensive considerations in a military sense (e. g. Shelmerdine, 1998, p. 87).
Restriction of access (from outside) and circulation (within) translates readily into space syntax terms
as a significant lowering of, on the one hand, the integration value of the carrier space, i.e. the outside
of the building, and, on the other, mean integration for the entire system. The carrier space does indeed
display a noticeable, if not dramatic, loss of integration, from 0.84 to 0.69 for the convex and 1.27 to 1.11
for the axial break-up; yet even these lowered values remain virtually identical or even slightly higher
than the mean for integration, calculated at 0.70 for the convex and 0.96 for the axial break-up in the
later state. If the carrier is as well integrated with the building as a whole as is the average space within
it, this hardly constitutes a defensive architecture. As to circulation within, the just cited mean values of
integration hardly change at all from the earlier state, for which they are calculated as 0.72 and 1.01 in
the axial and convex analysis respectively; in fact, if one of the aforementioned alternative suggestions for
the calculation of integration values (Teklenburg et al., 1993) is followed, this minimal drop is reversed
into an (equally insignificant) rise in integration (Thaler, 2005, p. 327).
This is remarkable not only in that it clearly contradicts (one of the underlying assumptions of) the
decline hypothesis, but also when viewed against relative proportions of space types, particularly the
increase of spaces of type b, 29% in the earlier and 38% in the later building state, and the concomitant
decrease of d-type ring-connectors, which account for 18% of all spaces in the earlier state, but only 9%
later on. It is not ease of movement that decreased, but options of route choice; i.e. circulation was not
restricted, but rather channelled. Channelling of traffic towards distinct routes is an aspect of the grow-
ing architectural differentiation of the palace complex and is particularly evident with regard to what
might be described as its service ‘wing’: If we compare the j-graph for the palace (Figure 16.4(e)) and a
mapping of the areas most quickly (i.e. with the least topological steps) reached from each of its three
points of access (Figure 16.4(c)), then an area of store rooms at and around the back of the palace’s main
building stands out as a coherent subsystem with only few connections to the remainder of the complex.
A j-graph constructed for access only through this ‘tradesmen’s entrance’ (as it was termed in another
earlier and rather perceptive study, Kilian, 1984, p. 43), i.e. omitting the two other access points, shows the
palace as a remarkably deep and inaccessible structure; clearly, the larger (and more representative part) of
the complex was not meant to be accessed from this direction.
If we look at how official visitors were meant to enter a Mycenaean palace (or, at least, the most high-
ranking visitors, since differentiations in rights of access seem to have held great importance), there is a
canonical route through first a propylon and then a courtyard (both elements could be repeated) into
the megaron; inside the megaron itself, there was first an open porch, from which a vestibule could be
accessed which in turn lead into the hearth/throne room. Although the latter, numbered as room 6 by
the excavators, was the most integrated a-type space, thus combining an accessible/commanding position
and privacy, in both the earlier and later state of the Pylos palace, it was only in the later state that the
topologically shortest route through the convex map into the throne room came to coincide with the
canonical route just set out (Figure 16.4(a–b)); concomitantly, VGA documents a shift of visual integra-
tion within the large courtyard in front of the main building from its sides to its centre and thus towards
the propylon. This may well be a case of a specific social practice, i.e. a canonical way of approaching
the ruler’s seat, becoming embodied in the (architectural but also highly) social structure of the palace
building, which then, of course, was instrumental in perpetuating it.
308 Ulrich Thaler

Another aspect of the growing differentiation of the palace complex besides such channelling can be
found in the comparison not of routes, but of individual spaces and none are more informative in this
regard than the major courts. While the earlier building state displayed a largely undifferentiated ring of
hypaethral spaces around the main building, three distinct and separate courtyards develop there in the
course of the 13th century, courts 58, 63 and 88 of the later building state (Figure 16.4(d)). Their crucial
role in the palace complex is documented by the fact that, of all convex spaces, the three display the high-
est values for local integration (58 > 63 > 88), connectivity (58 > 63 = 88) and control (58 > 88 > 63).
Clearly, together these were the circulation hubs of the later palace, but nonetheless their roles were not
one and the same, as a comparison between 58 and 63 in particular illustrates.
Court 58 displays a significantly lower depth from the carrier space, indeed it is a mere two steps
from two access points to the palace (out of a total of three, the third being the aforementioned ‘trades-
men’s entrance’) and no route from these two entrances into the deeper sections of the palace can bypass
58. Little surprisingly, the palace archive is nearby and what has been identified as a clearing-house for
the redistributive palace economy opens directly onto 58, which can be identified as the interface for
all official outside contacts of both political/ceremonial and formal economic nature (anything other
than deliveries of goods for consumption within the palace, it would seem). And yet, in terms of global
integration, i.e. in its relevance for circulation within the palace, 58 is eclipsed by court 63 as the most
highly integrated convex space of the entire complex. To add insult to injury, both courts can be associ-
ated with pantries containing, among other things, thousands of drinking vessels, presumably employed
during palatial feasts; but, by comparison with the kylikes apparently used in the more deeply sited and
thus apparently more exclusive court 63, those associable with 58 are of noticeably inferior quality, indi-
cating how architectural differentiation could be translated into social differentiations during specific
events hosted within the palace (Bendall, 2004). As to court 88, mapping those areas topologically more
closely associated with this courtyard rather than either 58 or 63 (Figure 16.4(d)) produces a result that is
almost completely congruent with the aforementioned mapping of primary access through the ‘trades-
men’s entrance’; court 88 was the hub of the service ‘wing’ and presumably no more than a staging area
in the context of feasts.

Conclusion
Given its underlying (and, it would appear, empirically proven) premise that a three-dimensional Euclid-
ian space can be reduced to a two-dimensional topological one and still be meaningfully analysed in social
terms, it should not surprise us that space syntax methodology is not difficult to apply, both in general
and in particular, i.e. to archaeological contexts (cf. Hacıgüzeller & Thaler, 2014). This ease of applica-
tion is further helped, to no small degree, by the fact that the Bartlett School of Architecture has made
fairly user-friendly analytical software available free of charge for academics, first with Alasdair Turner’s
Depthmap (Turner, 2011; cf. Turner, 2001b, 2004), which largely replaced an earlier bundle of Macintosh-
based programmes, and more recently with Tasos Varoudis’s depthmapX (Varoudis, 2012). It is so simple
(and, indeed, takes so little understanding of the underlying procedures) to produce a plausible(-looking)
output with just a few mouse-clicks, that anyone planning to work with space syntax more extensively
or in some depth should perhaps consider starting with a ‘manual’ analysis or two.
Any prospective user should also keep in mind that space syntax does not produce any meaningful
results in a vacuum. I have elsewhere (Thaler, 2006, 2018, pp. 8–26) proposed an analytical framework
that uses different levels of diachronic stability as a guiding principle to meaningfully relate different
perspectives on the social definition and the archaeological documentation of architectural spaces, includ-
ing space syntax. Yet a more general and two-fold caveat should be emphasized in the present context,
 Space syntax methodology 309

namely that both a critical assessment of the source materials, i.e. the plans intended for analysis, and a
considered contextualization of results are important and, at least in the latter case, indispensable steps in
archaeological studies employing space syntax methods. We are no longer in a position to see whether
the high integration value of space X, Y or Z in any building or settlement under analysis correlates with
actual movement patterns, but have to assume that it does based on the analogy with observations on
present-day contexts. Similarly, we cannot question occupants on what specific spaces are used for and
therefore will have to relate analytical results to archaeological indications of space use. Finds inventories
for specific spaces are the obvious example, but the study of wall-painting locations through space syntax
(Letesson, 2012) – and thus of a category of non-movable, ‘diachronically stable’ finds less prone to pre-
and postdepositional dislocation than most other finds – provides a good illustration that we need not
confine ourselves to the obvious.
That said, the fact remains – or comes into focus even more clearly – that space syntax approaches
entail high demands on archaeological data. This holds true with regard to both ‘coverage’ – understand-
ably, the analysis of incomplete building plans is not an issue widely discussed in the non-archaeological
space syntax community – and level of detail. Some of the most exciting approaches in archaeological
space syntax research, although ones whose potential may not have been fully realized in extant case
studies, are therefore those which explicitly address the weaknesses in archaeological data quality, e.g.
by harnessing the concept of topological genotypes in order to reconstruct incomplete building plans
(Romanou, 2007), by trying to open up the large-scale coverage of geophysical survey to space syntax
analysis (Spence-Morrow, 2009) or by aligning space syntax perspectives with data recovery methods
that promise very fine-grained information on space use in built contexts, such as micro-refuse analysis
(Milek, 2006).
In the light of these latter studies, it could be suggested that the greatest hope for space syntax in
archaeology does not lie in specialist desk- and literature-based studies, though given the inherently
comparative stance of space syntax their potential contribution remains great, but in research designs for
fieldwork that take into account the needs of topological analyses of social space, not in order to ‘cater
for’ specialists, but in order to enlist a further useful tool for the detailed published study that is the aim
and raison d’être of research excavations and surveys.

Notes
1 It should be noted that the use of the term ‘depth’ in the present introductory text differs slightly – and deliber-
ately – from much of the extant literature, where a wider meaning is adopted. Hence, what is here termed simply
‘depth’ may be read as ‘depth from carrier’ in more conventional terms, whereas what in the following will be
referred to as ‘path length’ or ‘step distance’, i.e. the distance between any two nodes in a system, will often be
described simply as ‘depth’. There is a clear logic in the latter usage in that, e.g. the mean depth of (or for) a given
node will indicate how deep the system is from that node, but the more descriptive designation ‘path length’ was
felt to offer a more intuitive appreciation of methodological foundations and is thus preferred here. Correspond-
ingly, in the formulae given in the text ‘MD’ can be read as either ‘mean distance’ (in the terms chosen in this paper)
or ‘mean depth’ (in the more conventional usage). For analytical purposes, calculating the integration (cf. below)
of the carrier will often be a strong alternative to considering the mean depth (from the carrier) of a system.
2 Further illustration of this point can be seen in deliberate divergences from the strict definition of convexity in
Figure 16.3(a). While it seems clear – to the author and hopefully the reader, too – that the insertion of a staircase
in the room labelled ’1’ breaks the latter up into two separate spaces, the non-convexity of rooms 5 and 9 was
considered too little pronounced to warrant subdividing these spaces. The most arbitrary decision was certainly
to subdivide room 6, which like room 1 houses a staircase in one corner, into two spaces in such a manner that
the larger one, room 6 a, ‘controls’ the door to corridor 3 at the cost of its strict convexity (rather than assign that
control to the ‘nook’ 6 b or sharing it between 6 a and 6 b). In the strictest sense, the floor area inside each door
opening would have to be considered a separate convex space; these connecting spaces would, coincidentally, paral-
lel the ‘connectors’ needed in the early space syntax software ‘Pesh’. Elsewhere, I have used the term “semiconvex
310 Ulrich Thaler

breakup” to indicate “a suitable compromise between the analysis of convex and bounded spaces in a complex
containing both roofed and open areas” (Thaler, 2005, p. 327; cf. Thaler, 2018), but arguably such a designation
could be considered to imply an impractically absolute concept of convexity.
3 In a similar vein, entropy, calculated through a logarithmic formula, and other measures derived from it were
studied, particularly in the context of VGA, for their potential to “give an insight into how ordered the system
is from a location“ (Turner, 2001b, p. 9); but while high entropy could be associated with even distributions of
path lengths from a given space to other spaces, a low entropy value for a space could either indicate many other
spaces in close proximity or the opposite, a clustering of spaces at a distance.
4 The case study briefly set out here is presented in more detail in: Thaler (2005, 2018, pp. 39–185) and Hacıgüzeller
and Thaler (2014). Its results are contextualized in: Thaler (2006, 2018). As also briefly discussed in n. 2, the con-
cept of convexity was applied with a deliberate degree of latitude in this case study, but corresponding terms like
‘convex space’, ‘convex break-up’ etc. are retained in their conventional form in the present introductory text.

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