Interpretation of Space Syntax in Higher Education: A Study of Functional Efficiency in Architecture Schools in Erbil

Abstract

Assessing a built environment’s functional performance and physical and psychological impact is essential for understanding its effect on users, particularly in higher education, where it informs the creation of effective learning spaces. This study aims to explore the application of Space Syntax Theory in a higher-educational context and examines the functional efficiency of three architecture schools in Erbil: Salahaddin University-Erbil, Koya University, and Cihan University-Erbil. Using a quantitative research paradigm, the study employs space-syntax methodologies, including axial map analysis and justified graphs, to evaluate key syntactical parameters such as mean depth, relative asymmetry (RA), real relative asymmetry (RRA), real ring-ness (R-value), and the difference factor (H*). The analysis, conducted via Depthmap X software, examines spatial permeability and connectivity within educational layouts, providing insights into their functional performance. The findings indicate that the architecture school at Cihan University-Erbil, characterised by a ring-like spatial structure, achieves a moderate level of functional performance, outperforming Salahaddin University-Erbil and Koya University. Moreover, productive spaces consistently exhibit higher functional performance than supportive spaces across all case studies. This research proposes a framework for optimising spatial configurations in higher education, providing evidence-based strategies to enhance functionality and promote best practices in educational architecture.

1. Introduction

Many theories and studies have investigated, examined, and evaluated the relationships between human experience and built environments from several perspectives, especially since the second half of the twentieth century; this reflects the complex interplay between human behaviour, social structures, cultural values, and physical spaces. These interdisciplinary theories draw from psychology, sociology, anthropology, and environmental studies to understand and enhance the human experience within architectural contexts. The Prospect–Refuge Theory, Environmental Psychology, Biophilic Design Theory, the Theory of Affordances, Space Syntax Theory, and the concepts of Jane Jacobs’s work and Place Attachment are among the research frameworks that emphasise the importance of considering psychological, social, and cultural factors in architectural design to create environments that are responsive to human needs and aspirations. The built environment can be assessed through three performance criteria: health, function, and psychology [1]. The functionality of the built environment is intrinsically associated with the optimisation of operational effectiveness, the efficiency of work processes, the adequacy of spatial provisions, and the deliberate spatial integration of interrelated functional zones [1]. Architects have long underscored the vital importance of a building’s function, ensuring that structures serve their intended purposes and balance structural integrity and aesthetic appeal. The principle of “form follows function”, articulated by Louis Sullivan, reinforces the notion that architectural design should emerge from a building’s utility, harmonising aesthetics with practical requirements [2]. Moreover, functional performance evaluation is a central focus of the Post-Occupation Evaluation Framework. This approach distinguishes itself from other evaluation methods by prioritising the needs of building occupants, considering health, functionality, and the social, psychological, and cultural dimensions of performance [3]. Various researchers have conducted evaluations of the functional performance of diverse structures employing space-syntax methodology. Their investigations encompass many building types, including residential dwellings [4], schools [5], libraries [6], and higher-education facilities [7,8].

Space syntax is a theoretical framework and analytical method developed by Bill Hillier, Julienne Hanson, and their colleagues at University College London (UCL) in 1980 that examines the spatial configuration of built environments and the impacts of these configurations on human behaviour and social interactions [9]. The theory was generated after studying many community settlements and towns in distinct locations and their social and community lifestyles [9]. Space-syntax analysis uses mathematical and graphical techniques to study how spatial layouts of urban areas and building structures influence movement patterns, accessibility, and social connectivity [10]. This theory has been applied in urban planning and architecture to design spaces facilitating social interaction, accessibility, and wayfinding.

The Space Syntax Theory depends on graph theory in presenting the spatial structure of buildings and urban areas [10]. Based on this theory, a circle presents the individual spaces (convex space), and a line represents the permeability of access among spaces in the graph, which is called a justified graph [10], as illustrated in Figure 1. This graph presentation is crucial to presenting the spatial configuration and identifying the morphological forms of the building layouts [11]. Space Syntax Theory will investigate the physical permeability and visual connectivity among the spaces within the built environment. These physical permeability relationships among spaces have been classified into four categories: symmetry, asymmetry, distributed, and undistributed; this is demonstrated in Figure 1 [10]. Studying the syntactic properties related to spatial structure in buildings and urban areas is significant in understanding the spatial relationships within the built environment that identify the social and cultural context of the layout [12]. Historically, researchers developed several variables to quantify these spatial properties, such as integration value and choice; the former is valuable for studying the degree of integration and segregation of spaces within the building system [11]. The latter is significant for studying the distributed and non-distributed properties of building spatial layout by specifying the tree and ring structure of the spatial layout [11].

At UCL, researchers have developed the Depthmap X software, a pivotal tool used in space syntax for analysing the structure of spatial configuration [12]. This platform can deliver several analysis types: axial map, visibility graph analysis (VGA), segment, and agent-based analysis. These analyses are essential for studying accessibility, movement patterns, pedestrian flow, visibility, and other spatial properties that have social and cultural meaning. Recently, researchers have used the Space Syntax Theory to investigate how the spatial arrangement of higher-education environments can potentially revolutionise learning processes and elevate students’ experiences [12]. The incorporation of advanced tools, such as space-syntax techniques, is crucial for optimising functional efficiency and ensuring user-centred design. By rigorously analysing spatial configurations and environmental interactions, these methods enhance adaptability, operational performance, and sustainability, particularly in academic settings. This study, employing an analytical-based approach with space syntax, aims to examine spatial layouts’ functional performance in architecture schools in Erbil. The goal is to offer valuable insights that could sustain and optimise the design of future higher-education facilities.

2. Literature Review

Increasingly, many researchers are adopting space-syntax theory approaches to study the relationships among higher-education built environments, their urban contexts, and students’ experiences. Employing this theory in this context takes two forms.

2.1. University Campus Level

The Space Syntax Theory has been widely applied at the university campus level, focusing on the interrelationships between campuses and their urban contexts, sustainability aspects, and pedestrian environments (Table 1). Mohammed and Ukai [13] posit that the geographical positioning of university campuses exerts a more considerable influence on urban development patterns than do the openness characteristics of the campus itself. Their analysis employed syntactical measures, including connectivity, integration, and choice indices, to quantify the built environment’s properties [13]. Soares et al. [14] investigated the impact of public spaces on creativity at the University of Groningen’s Zernike campus, conceptualising creativity as a fourth dimension of sustainability. Their findings have significant practical implications, proving that creative potential is influenced not only by the accessibility of public spaces and street segments but also by the synergistic combination of active land use and diverse activities, such as cafés, restaurants, green pathways, and urban seating arrangements [14].

Furthermore, researchers have utilised space-syntax measurements to evaluate the suitability and efficiency of pedestrian routes within university campuses. Khorsheed and Goriel [15] specifically examined the layout and quality of pedestrian pathways in the primary campus of Duhok University in Duhok City. Their study emphasised the importance of the enhancement of pedestrian routes and advocating for increased student awareness of active transportation modes’ physical and psychological benefits [15]. Similarly, Al-Ahbabi and Al-Alwan [16] investigated the deficiencies in the pedestrian environment within the Jadiriya complex at the University of Baghdad, Iraq. Their research underscored the importance of segregating pedestrian and vehicular traffic, finding areas with clear intersections, and pinpointing the primary causes of traffic accidents [16].

Space-syntax analysis has also been employed to compare and show an influence of the social open spaces within university campuses [17,18]. Many of these studies adopted a mixed-methods approach, integrating space-syntax methodologies with qualitative research techniques. Moreover, as illustrated in Table 1, a predominant use of axial analysis maps was seen in evaluations of the spatial structures of university campuses.

Table 1. A thematic analysis of the space-syntax interpretations of university campuses. (Source: Authors).

Authors	Country	Studied Context	Research Method	Deductive Code	Analysis Type	Space-Syntax Measurements
Abu Elkhair et al., 2023 [17]	Egypt	American University in Cairo	Mixed methods	Enhancing the social quality	Axial map AVG Agent Simulation	(Connectivity) (Integration, connectivity) (Gate count analysis) [17]
Al-Ahbabi and Al-Alwan, 2023 [16]	Iraq	Jadiriya Complex—University of Baghdad	Mixed methods	Enhancing the pedestrian Safety	Axial map	(Integration index) [16]
Mohammed and Ukai, 2021 [13]	Japan	Kyushu University—Ohashi campus and Ito campus	Quantitative	The impact of university campuses on urbanisation	Segment	(Angular segment analysis) [13]
Khorsheed and Goriel, 2021 [15]	Iraq	University of Duhok	Mixed methods	Pedestrian satisfaction as to walkability	Axial map	(Connectivity, integration and choice) [15]
Soares et al., 2020 [14]	The Netherlands	The ‘Dependent Urban Fabric’ and the ‘Autonomous Urban Fabric University of Groningen’	Mixed methods	Relationship between spatial configuration and creativity	Segment	(Angular choice measure) [14]
Yildiz et al., 2020 [18]	The Netherlands	Utrecht University—Campus De Uithof	Mixed methods	Relationship between spatial configuration and publicness	Axial map VGA	(Local axial map and visibility map) [18]
Lo et al., 2015 [19]	Taiwan	Tunghai University	Mixed methods	Sustainable campus and wayfinding efficiency	Agent-based	(Hot sport target base) [19]

Table 1. A thematic analysis of the space-syntax interpretations of university campuses. (Source: Authors).

Authors	Country	Studied Context	Research Method	Deductive Code	Analysis Type	Space-Syntax Measurements
Abu Elkhair et al., 2023 [17]	Egypt	American University in Cairo	Mixed methods	Enhancing the social quality	Axial map AVG Agent Simulation	(Connectivity) (Integration, connectivity) (Gate count analysis) [17]
Al-Ahbabi and Al-Alwan, 2023 [16]	Iraq	Jadiriya Complex—University of Baghdad	Mixed methods	Enhancing the pedestrian Safety	Axial map	(Integration index) [16]
Mohammed and Ukai, 2021 [13]	Japan	Kyushu University—Ohashi campus and Ito campus	Quantitative	The impact of university campuses on urbanisation	Segment	(Angular segment analysis) [13]
Khorsheed and Goriel, 2021 [15]	Iraq	University of Duhok	Mixed methods	Pedestrian satisfaction as to walkability	Axial map	(Connectivity, integration and choice) [15]
Soares et al., 2020 [14]	The Netherlands	The ‘Dependent Urban Fabric’ and the ‘Autonomous Urban Fabric University of Groningen’	Mixed methods	Relationship between spatial configuration and creativity	Segment	(Angular choice measure) [14]
Yildiz et al., 2020 [18]	The Netherlands	Utrecht University—Campus De Uithof	Mixed methods	Relationship between spatial configuration and publicness	Axial map VGA	(Local axial map and visibility map) [18]
Lo et al., 2015 [19]	Taiwan	Tunghai University	Mixed methods	Sustainable campus and wayfinding efficiency	Agent-based	(Hot sport target base) [19]

2.2. Higher-Education Building Level

Researchers have employed different space-syntax approaches to explore how the layouts of educational facilities affect educational experiences and social interactions (

Table 2. A thematic analysis of the space-syntax interpretations of higher-education buildings. (Source: Authors).

Authors	Country	Studied Context	Research Method	Deductive Code	Analysis Type	Space-Syntax Measurements
Ji et al., 2023 [8]	China	School of Architecture, South China University of Technology	Quantitative	The effects of spatial layout on peer academic support relationships	Angular segment Step depth	(Integration-global scale) (Metric distance and visual distance) [8]
Safizadeh, 2023 [21]	Malaysia	Four student-residence buildings in the U.S.A.	Quantitative	Circulation complexity	Axial map VGA Isovisit Agent-based	(Integration and connectivity) (Integration and connectivity) (Isovisit measure) (Movement pattern) [21]
El Samaty et al., 2023 [7]	Saudi Arabia	The building of the College of Architectural Engineering and Digital Design at Dar Al Uloom University	Quantitative	The impacts of glazed barriers on visual and functional performance	Axial map VGA Local measurement	(Integration, choice, and intelligibility) (Integration and choice) (Clustering coefficient, visual control, visual entropy, through vision, and connectivity) [7]
Zhang and Cui, 2022 [20]	China	Three historical groups of laboratories	Quantitative	Relationship between scientific research activities and spatial forms	Axial map Convex map Justified graph	(Integration (HH), RA, R-value, distributed index, and H*) [20]
Sanni-Anibire et al., 2018 [22]	Saudi Arabia	Eight university laboratories	Quantitative	The functional performance of laboratories	Axial map Justified Graph	(Mean depth, RA, and H*) (R-value) [22]
Siramkaya and Aydin, 2017 [23]	Turkey	Faculty of Engineering—Selcuk University	Mixed methods	The effect of spatial configuration on social interaction	Syntax 2D	(Mean depth, connectivity, integration-n, isovisit area, isovisit perimeter, and circular parameters) [23]
Wu et al., 2017 [24]	England	Educational building-Nottingham University	Mixed methods	Spatial configuration shapes student social and informal learning activities	Convex map graph	(Integration value) [24]

). Zhang and Cui [20] employed space-syntax techniques to examine the spatial structure of nine historical and contemporary university laboratories. Their investigation reveals that scientific research has transitioned through multiple phases and that the scientific paradigm has a profound and significant influence on the spatial organisation of scientific research buildings [20]. Moreover, the spatial configuration of scientific research spaces during different periods manifests unique syntactic outcomes and topological structures. Ji et al. [8] emphasise the significance of the spatial layout of the learning environment in cultivating peer-academic support relationships. They also provide recommendations for university administrators and architects to consider for enhancing these spaces [8].

Additionally, applying space-syntax techniques has offered practical insights into the circulation efficiency and functional performance of various educational building layouts. For instance, Safizadeh [21] studies four student residence buildings in the USA, including courtyard-shaped, figure-eight-shaped, U-shaped, and double L-shaped layouts, revealing that the courtyard-shaped and figure-eight-shaped designs showed the highest circulation efficiency. Conversely, the U-shaped and double L-shaped plans showed the weakest circulation performance, highlighting the importance of layout design in enhancing circulation efficiency [21]. El Samaty et al. [7] state that glazed barriers will improve the functional performance of transition spaces by increasing visual accessibility and promoting smooth movement. Moreover, Sanni-Anibire et al. [22] affirm that the spatial arrangement of space can affect the operational effectiveness of academic and research laboratories. This was proved by comparing the laboratory layouts using spatial syntax measurements [22].

Recent research has investigated the impact of spatial configuration in higher-education environments on social interaction, yielding several significant findings. The parameters of spatial syntax serve as a valuable methodological framework for identifying architectural characteristics that facilitate social engagement [23]. Furthermore, the configuration of an environment can significantly influence the frequency of social interactions among students and their involvement in informal learning activities [24]. Most of these studies have employed a quantitative research approach to effectively explore and compare the spatial configuration of various higher-education building facilities (Table 2).

There is a noticeable gap in the existing literature concerning evaluating the functional performance of diverse spatial configurations in educational buildings. This factor is pivotal for optimising the learning environment. Previous studies on functional efficiency have predominantly concentrated on specific areas within the school of architecture buildings and laboratory facilities. This research evaluates the functional efficiency of various categories of learning spaces specific to architectural education across three universities in Erbil. Given the interdisciplinary nature of architectural education, a broader range of learning spaces is required compared to other disciplines. These spaces encompass distinct areas for design, lectures, individual work, collaboration, and the presentation of design projects [25]. Assessing the functionality of these spaces is imperative for enhancing the quality of architectural education and bolstering students’ motivation and overall educational experience. The study aims to establish a framework for utilising space-syntax analysis to discern the functional effectiveness of three architecture schools in Erbil.

3. Methods

3.1. Study Design and Method

This study used two approaches to achieve its objectives. First, the authors reviewed the existing literature on space-syntax employment in higher-education facilities. Second, space-syntax analysis was used to examine the functional efficiency of three architecture schools in Erbil.

The researchers used the space-syntax approaches to analyse buildings and urban spaces to investigate human behaviour and social experience [10]. Most studies adopted space syntax to explore the social interaction patterns behind house spatial configurations by judging their spatial properties [4,11,26]. The current research commenced with a comprehensive review of the pertinent literature encompassing relevant topics and studies to profoundly understand the issues, pinpoint any knowledge gaps, and formulate the study’s design framework. Subsequently, a study framework was devised to scrutinise the functional efficiency of the chosen higher-education case studies.

3.2. Study Framework

The authors created an applicable framework for the study based on their interpretation of space syntax’s application in the built environment. The framework includes axial analysis and a justified graph. This study examined the functional efficiency in three architecture schools through several syntactic measurements, namely, mean depth, RA, RRA, R-value, and H*. The school’s layout was carefully examined and analysed using the Depthmap X program to assess its spatial organisation. The justified graph was constructed based on the permeability relationships among spaces, providing valuable insights into the flow and connectivity within the school’s design.

The authors adopted this framework for its proven efficacy, as validated by prior studies assessing functional performance within the built environment. Furthermore, the framework enables the analysis of functionality at both the individual-space and categorical levels. The effectiveness of those syntactic measurements has been highlighted in evaluations of functional efficiency in traditional and contemporary houses [4]. Furthermore, this set of variables was used to compare the functional performance of some university libraries in Saudi Arabia [18]. The chosen syntactical parameters in this study quantify syntactical properties related to individual spaces within a spatial complex. These properties include integration, segregation, and the spatial structure pattern of the entire spatial complex, and they directly impact the functional performance of the space.

Table 3. Implications of high and low values of selected syntactical variables. (Source: Adapted by authors).

Item	High Values Implication	Low Values Implication
RA	High values indicate a high degree of segregated space and a high degree of privacy.	Low values indicate the integrated degree of space and the highly public nature of the space.
RRA	The most-segregated spaces have an RRA value equal to or greater than 1, reflecting the higher degree of segregation. The best-segregated spaces can be classified as the lowest-scoring functional-performance spaces.	RRA values between 0.4 and 0.6 reflect the highest degree of integration. The best-integrated spaces can be classified as highly functional performance spaces.
H*	H* = 1 corresponds to a minimal functional difference or no functional difference, which reflects the low functional efficiency in spatial complexes.	H* = 0 corresponds to the maximum and high functional differences, reflecting the high functional efficiency of the spaces.
R-value	Where the R-value is greater than 1, its distributed nature indicates high flexibility (functional efficiency) and suggests the ring structure of spatial configuration.	An R-value of less than one indicates that the spatial system has a tree-like structure, suggesting the lack of distributed news and the increased depth of spaces within the built environment.

outlines the implications of the low and high values for the syntactical variables. The syntactical characteristics have been described below.

3.2.1. The Integration Measure (RA)

The measure of relative asymmetry generalises this metric by comparing how deep the system is, measured from a particular point, with how deep or shallow it theoretically could be. The most insignificant depth exists when all spaces are directly connected to the original space, and the most significant when all spaces are arranged in a unilinear sequence away from the original space, i.e., every additional space in the system adds one more level of depth [10]. The following equation calculates the RA value by dividing the mean depth in individual spaces by the total number of spaces, without route space [10] (p. 108).

Relative Asymmetry (RA) = 2(MD − 1)/(K − 2)

(1)

where the MD is the mean depth of space and K is the total number of spaces in the system. The RA value will vary between 1 and 0 [10].

3.2.2. RRA

Among the other syntactic properties that describe the individual space relationship within the built environment is the RRA. This syntactic measure helps quantify the integration value of spaces and enhances the categorisation of spaces according to integration value. The RRA is the ratio of relative asymmetry of space within the building system to its D-values for k (total number of spaces within the system) for diamond-shaped complexes, as shown in Equation (2) [10] (p. 133).

Real Relative Asymmetry (RRA) = (RA)/Dk

(2)

where RRA: the real relative asymmetry of the space; RA: the relative asymmetry of the space; and Dk: relative asymmetry of space, from a diamond-shaped graph.

As a result of having several space roots, the RRA value for each space within the building system will be greater than 1 and within the range of 0–3. This description helps determine the integrated and segregated space within the building system. Furthermore, those integration values are also significant for knowing the sequence of spaces, based on the integrated level. In addition, the functional efficiency of spaces can be determined based on the RRA values, which reflect the relationship between spaces in the building layout [26].

3.2.3. H*

Most spatial complexes have discrepancies in integration values across distinct spaces. These divergences play pivotal roles in elucidating the representation of cultural and social relations within spatial environments [11]. The degree of difference between three or more integration values of space is called the difference factor, as demonstrated in Equation (3) [11] and [27] (p. 31).

H = −(a/t × In (a/t) + b/t × In (b/t) + c/t × In(c/t))

(3)

where H is the un-relativized difference factor for three spaces a, b and c in the configuration and t is the sum of the three spaces, that is, t = Σ(a + b + c). H can be relativized between In2 and In3 to obtain the relative difference (H*), as illustrated in Equation (4).

The high difference-factor values indicate minimal disparities in integration values and the absence of functional differences among spaces. Conversely, low values denote substantial variances in integration values and significant functional disparities among spaces [26] and [27] (p. 31).

H* = (H − In2)/(In3 − In2)

(4)

3.2.4. R-Value of the Spatial System

Integration has been proposed as a syntactic measure for evaluating symmetry–asymmetry within spatial systems. Additionally, a relative “ringiness” measure has been suggested for assessing properties of “distributedness” and “non-distributedness” [26]. The distributedness properties among spaces exist when there is more than one accessible route among spaces, reflecting the ringiness-based structure of the spatial configuration [10]. In contrast, the non-distributedness properties of spatial configuration exist where the spaces connect only through one accessible route [10]. Then, the relationship among spaces can be presented as a tree-like structure. The relative ringiness value can be determined using Equation (5) [4] (p. 140).

Relative ringiness (R-value) = (L + 1)/K

(5)

where R: relative ringiness; L: total number of lines of links between spaces in the justified graph; and K: number of spaces (nodes) in the spatial system.

The R-value will vary according to the number of spaces (convex space) and the relationship among spaces, such as connectivity and accessibility. The R-values vary around the number 1, with values greater than 1 corresponding to a high degree of ringiness and a distribution characteristic of a spatial system (“ringy” structure) [21].

3.3. Case Study Selection and Description

Three architecture school buildings in Erbil are under examination: the architecture school building at Salahaddin University-Erbil, the architecture school at Cihan University-Erbil, and the architecture school at Koya University. These schools were designed by professional architects in each region specifically for architecture education and have been in use for over 10 years. They provide the necessary spaces based on established standards, such as the area required per student, lighting conditions, and other specifications enumerated in educational guidelines. These schools are considered good design examples within their institutional contexts. None of the buildings are exclusively dedicated to the use of the architecture school; in all three cases, the architecture school buildings have other scientific departments co-located within them. To conduct a detailed analysis of the facilities in these school buildings, the researchers classified the spaces into two main categories, productive and supportive, based on Kruger’s (1992) classification of learning spaces in architecture schools as reported by Wang [28]. The spaces were then further sub-classified within each category based on the nature of activities in those spaces, as illustrated in

Table 4. The classification of spaces within the architecture school. (Source: Authors).

Number	Space Categories	Sub-Category	Activity Category	Space Names
1	Productive Spaces	Primary Spaces	Programmed	Design studios.
		Secondary Spaces	Programmed	Lecture halls, lecturers’ offices, library, laboratories, and workshops.
		Non-programmed activity		Corridors, atriums, cafeteria, and stairs.
2	Supportive Spaces	Programmed activity		Administration area.
		Non-programmed activity		Toilets and storage spaces.

.

4. Results

The authors employed axial analysis and justified-permeability graphs to evaluate the functional performance of the spatial configuration in three case studies in Erbil. This analysis obtained several syntactical characteristics for each case study, such as mean depth, RA, RRA, R-value, and H*. The four variables have been quantified based on an axial-map analysis for each case study. This process includes the analysis of school layouts through the Depthmap X software (https://www.spacesyntax.online/software-and-manuals/depthmap/, accessed on 27 October 2024), which depends on a convex map generated for each case study. Some details about the spatial configuration analyses for all case studies have been illustrated in Figure 2, Figure 3 and Figure 4. Further details of these convex maps, and the Depthmap X files, are available by means of a website link provided below. At the same time, the latter variable was calculated from a justified graph for each study. The authors examined the functional efficiency of each case study through these syntactical measurements, as clarified below. This analysis is crucial for evaluating functional efficiency with respect to distinct space categories.

4.1. Case Study One: Architecture School of Salahaddin University-Erbil

4.1.1. Productive Space Category

The syntactical measurement variables (mean depth, RA, and RRA values) derived from the axial analysis exhibit variations across the learning spaces within the architecture school at Salahaddin University-Erbil, as delineated in

Table 5. Demonstrated mean depth, RA, and RRA values for the productive spaces at the architecture school at Salahaddin University-Erbil. (Source: Authors).

Space Category		Space Name	Connectivity	Mean Depth	RA	RRA
Programmed activities	Primary Spaces	Design Studio No.01-DAE 1 G.F. 2	1	4.935	0.074	0.924
		Design Studio No.02-DAE G.F.	1	6.657	0.106	1.329
		Design Studio No.03-DAE G.F.	1	5.722	0.088	1.109
		Design Studio No.04-DAE G.F.	1	6.657	0.106	1.329
		Design Studio No.01-DAE F.F.	2	5.102	0.077	0.963
		Design Studio No.02-DAE F.F.	1	5.102	0.077	0.963
		Design Studio No.03-DAE F.F. 3	2	6.019	0.094	1.179
		Design Studio No.04-DAE F.F.	1	7.833	0.128	1.605
		Minimum	1	4.935	0.074	0.924
		Maximum	2	7.833	0.128	1.605
		Mean	1.125	6.003	0.094	1.175
	Secondary Spaces	Lecture Hall No.01-DAE G.F.	1	5.898	0.092	1.150
		Lecture Hall No.02-DAE G.F.	1	5.898	0.092	1.150
		Lecture Hall No.03-DAE G.F.	1	5.880	0.091	1.146
		Computer Hall No.01-DAE G.F.	1	6.833	0.109	1.370
		Internet Hall No.01-DAE G.F.	1	6.833	0.109	1.370
		Lecture Hall No.04-DAE G.F.	1	4.963	0.074	0.931
		Library-DAE G.F.	1	4.963	0.074	0.931
		Lecturer Office No.01-DAE-G.F.	1	5.759	0.089	1.118
		Seminar Hall-No.01-DAE G.F.	1	5.907	0.092	1.153
		Lecturer Office No.02-DAE G.F.	1	6.657	0.106	1.329
		Lecturer Office No.03-DAE G.F.	1	6.657	0.106	1.329
		Lecturer Office No.04-DAE G.F.	1	5.722	0.088	1.109
		Lecturer Office No.05-DAE G.F.	1	5.722	0.088	1.109
		Lecturer Office No.06-DAE G.F.	1	6.657	0.106	1.329
		Lecturer Office No.01-DAE F.F.	1	6.694	0.106	1.337
		Lecturer Office No.02-DAE F.F.	1	6.694	0.106	1.337
		Lecturer Office No.03-DAE F.F.	1	6.694	0.106	1.337
		Lecturer Office No.04-DAE F.F.	1	6.694	0.106	1.337
		Lecturer Office No.05-DAE F.F.	1	5.102	0.077	0.963
		Lecture Hall No.01-DAE F.F.	1	5.102	0.077	0.963
		Lecturer Office No.06-DAE F.F.	1	6.037	0.094	1.183
		Lecturer Office No.07-DAE F.F.	1	5.102	0.077	0.963
		Freehand Hall No.01-DAE F.F.	1	5.102	0.077	0.963
		Lecturer Office No.08-DAE F.F.	1	7.833	0.128	1.605
		Lecturer Office No.09-DAE F.F.	1	7.833	0.128	1.605
		Minimum	1	4.963	0.074	0.931
		Maximum	1	7.833	0.128	1.605
		Mean	1	6.130	0.096	1.205
Non-programmed@activities		Space Root	3	5.685	0.088	1.100
		Main Entrance for DAE	2	5.685	0.088	1.100
		Secondary Entrance for DAE	2	4.861	0.072	0.907
		Main Entrance for DSE 4	2	6.546	0.104	1.303
		Front Entrance Hall for DAE	3	4.806	0.071	0.894
		Hall No.01-DAE G.F.	9	3.972	0.056	0.698
		Hall No.02-DAE G.F.	4	4.907	0.073	0.918
		Hall No.03-DAE G.F.	3	4.889	0.073	0.913
		Back Entrance Hall for DAE G.F.	2	4.870	0.072	0.909
		Hall No.04-DAE G.F.	3	5.843	0.091	1.137
		Staircase-DAE-flight-1	2	4.157	0.059	0.742
		Staircase-DAE-flight-2	2	4.287	0.061	0.772
		Main Central Hall-01 G.F.	7	3.944	0.055	0.692
		Hall No.06-DAE G.F.	2	4.917	0.073	0.920
		Front Entrance Hall-DSE	2	7.407	0.120	1.505
		Hall No.01-DSE G.F.	2	7.861	0.128	1.611
		Staircase-DSE-flight-1	2	7.435	0.120	1.511
		Staircase-DSE-flight-2	2	6.611	0.105	1.318
		Central Main Hall No.02 G.F.	6	4.731	0.070	0.876
		Entrance Hall for Design Studio-02 G.F.	4	5.667	0.087	1.096
		Entrance Hall for Design Studio-04 G.F.	4	5.667	0.087	1.096
		Main Central Staircase-Flight-1	3	4.000	0.056	0.705
		Main Central Staircase-Flight-2	2	4.185	0.060	0.748
		Main Central Staircase-Flight-3	2	4.861	0.072	0.907
		Hall No.01-DSE-F.F.	4	5.722	0.088	1.109
		Hall No.02-DSE-F.F.	1	6.713	0.107	1.342
		Hall No.03-DSE-F.F.	1	6.713	0.107	1.342
		Hall No.01-DAE-F.F.	13	4.111	0.058	0.731
		Hall No.02-DAE-F.F.	2	4.898	0.073	0.916
		Hall No.03-DAE-F.F.	8	5.704	0.088	1.105
		Staff Cafeteria-DAE F.F.	1	6.694	0.106	1.337
		Examination Room-DAE F.F.	1	6.694	0.106	1.337
		Entrance Hall for Design Studio-03 F.F.	3	5.046	0.076	0.950
		Store for Design Studio-No.03-DAE F.F.	1	7.009	0.112	1.411
		Hall No.04-DAE-F.F.	2	5.009	0.075	0.942
		Hall No.05-DAE-F.F.	3	4.991	0.075	0.937
		Store Hall No.01-DAE F.F.	1	5.981	0.093	1.170
		Hall No.06-DAE-F.F.	2	5.907	0.092	1.153
		Entrance Hall for Design Studio-04 F.F.	4	6.843	0.109	1.372
		Minimum	1	3.944	0.055	0.692
		Maximum	13	7.861	0.128	1.611
		Mean	3.128	5.534	0.085	1.065

¹ DAE: Department of Architectural Engineering, ² G.F.: Ground Floor,³ F.F.: First Floor, ⁴ DSE: Department of Software Engineering.

. The authors’ upcoming presentation will involve a comprehensive analysis and interpretation of these vital measurements.

In the category of primary spaces designated for programmed activities, the analysis reveals that two design studios demonstrate a moderate level of functional performance, as reflected by a mean depth value of 5.102, RA value of 0.077, and RRA value of 0.963. Conversely, two design studios within the same category exhibit the lowest level of functional performance, with a mean depth value of 6.657, RA value of 0.106, and RRA value of 1.329. The average mean depth value of 6.003, RA value of 0.094, and RRA value of 1.175 for spaces in this category suggest a range of functional efficiency from low to medium.

The results of the analyses of secondary spaces as productive spaces designated for specific activities reveal variations in their design across the different spaces for diverse activities, as outlined in Table 5. The library demonstrates the highest level of integration within this classification, characterised by a mean depth value of 4.963, an RA value of 0.074, and an RRA value of 0.931, signifying significant functional performance. Conversely, Lecture Hall No.04 G.F., Lecture Hall No.01 F.F., and the Freehand Hall on the first floor exhibit moderate performance. The metrics for Lecturer Offices indicate high privacy but lower functional efficacy. The average syntactical value for this space category (mean depth value of 6.130, RA value of 0.096, and RRA value of 1.205) reflects a predominance of lower functional performance, marginally lower than the functional efficiency of the primary spaces appointed for programmed activity.

The various productive spaces chosen for non-programmed activities show distinct syntactical values. The main central hall, No.01 G.F., demonstrates a mean depth value of 3.944, RA value of 0.055, and RRA value of 0.692. Concurrently, Hall No.01-DAE G.F. has a mean depth value of 3.973, RA value of 0.056, and RRA value of 0.698, representing the lowest integration values within this category. This measurement shows an intermediate to high level of functional performance, which is significant for understanding the user experience. Conversely, Hall No.02-DSE F.F. and Hall No.03-DSE F.F. have mean depth values of 6.713, RA values of 0.107, and RRA values of 1.342, thereby classifying them as the most segregated spaces in this category, symbolising a low level of functional performance. The average syntactical values of these spaces, with a mean depth value of 5.534, RA value of 0.085, and RRA value of 1.065, reflect their integrated properties, and their functional performance oscillates between a medium and low level.

4.1.2. Supportive-Space Category

The syntactical measurements of various office spaces reveal differences in privacy levels and functional performance (

Table 6. Shows the mean depth and RA and RRA values for the supportive spaces at the architecture school at Salahaddin University-Erbil. (Source: Authors).

Space Category	Space Name	Connectivity	Mean Depth	RA	RRA
Programmed activities	Administration Hall-DAE G.F.	6	4.769	0.070	0.885
	Head of DAE-office No.1 G.F.	2	5.741	0.089	1.113
	Head of DAE-office No.2 G.F.	2	6.713	0.107	1.342
	Secretary DAE-office G.F.	2	5.741	0.089	1.113
	Reporter Room-DAE G.F.	1	5.759	0.089	1.118
	Staff Room No.01-DAE G.F.	1	5.759	0.089	1.118
	Minimum	1	4.769	0.070	0.885
	Maximum	6	6.713	0.107	1.342
	Mean	2.33	5.741	0.089	1.113
Non-programmed activities	W.C. Students: Male-DAE-G.F.	2	5.787	0.089	1.124
	W.C. Students: Male-DAE-G.F.	4	6.722	0.107	1.344
	W.C. Students: Male-DAE-G.F.	1	7.713	0.125	1.577
	W.C. Students: Male-DAE-G.F.	1	7.713	0.125	1.577
	W.C. Students: Male-DAE-G.F.	1	7.713	0.125	1.577
	W.C. Students: Female-DAE-G.F.	2	5.722	0.088	1.109
	W.C. Students: Female-DAE-G.F.	4	6.657	0.106	1.329
	W.C. Students: Female-DAE-G.F.	1	7.648	0.124	1.561
	W.C. Students: Female-DAE-G.F.	1	7.648	0.124	1.561
	W.C. Students: Female-DAE-G.F.	1	7.648	0.124	1.561
	W.C.-Staff: Female-DAE G.F.	2	5.704	0.088	1.105
	W.C.-Staff: Female-DAE G.F.	3	6.657	0.106	1.329
	W.C.-Staff: Female-DAE G.F.	1	7.648	0.124	1.561
	W.C.-Staff: Female-DAE G.F.	1	7.648	0.124	1.561
	Internal Courtyard-G.F.	1	4.935	0.074	0.924
	Service Room No.01-DAE G.F.	1	6.657	0.106	1.329
	W.C.-Staff Male-DAE F.F.	2	6.639	0.105	1.324
	W.C.-Staff Male-DAE F.F.	3	7.593	0.123	1.548
	W.C.-Staff Male-DAE F.F.	1	8.583	0.142	1.781
	W.C.-Staff Male-DAE F.F.	1	8.583	0.142	1.781
	W.C. Student Female-DAE F.F.	2	5.009	0.075	0.942
	W.C. Student Female-DAE F.F.	2	5.926	0.092	1.157
	W.C. Student Female-DAE F.F.	4	6.861	0.110	1.377
	W.C. Student Female-DAE F.F.	1	7.852	0.128	1.609
	W.C. Student Female-DAE F.F.	1	7.852	0.128	1.609
	W.C. Student Female-DAE F.F.	1	7.852	0.128	1.609
	W.C. Student Male-DAE F.F.	2	5.926	0.092	1.157
	W.C. Student Male-DAE F.F.	4	6.861	0.110	1.377
	W.C. Student Male-DAE F.F.	1	7.852	0.128	1.609
	W.C. Student Male-DAE F.F.	1	7.852	0.128	1.609
	W.C. Student Male-DAE F.F.	1	7.852	0.128	1.609
	Minimum	1	4.935	0.074	0.924
	Maximum	4	8.583	0.142	1.781
	Mean	1.742	7.075	0.114	1.427

). Notably, the office of the Head of the Architecture School, office no.01 G.F.; Secretary of DAE office G.F.; Staff room No.01 G.F.; and the DAE reporter office exhibit similar syntactical values (mean depth: 5.741, RA: 0.089, and RRA: 1.113), indicating segregated spaces and sufficient privacy, with a functional performance ranging from low to medium. Conversely, the administration hall—DAE G.F. displays distinct values (mean depth: 4.769, RA: 0.070, and RRA: 0.885), suggesting integrated properties and medium to high functional performance. The overall statistical average (mean depth: 5.741, RA: 0.089, and RRA: 1.113) signifies segregated properties and low to medium functional performance across the spaces in this category.

The supportive spaces appointed for non-programmed activities exhibit a predominance of convex shapes. The average statistical parameters for these spaces show a mean depth of 7.075, RA of 0.114, and RRA of 1.427. These spatial categories manifest the highest syntactic values, denoting their segregated attributes and elevated privacy levels. However, they also signify a diminished functional efficiency within these spaces.

4.1.3. Overall Functional Performance of the School

The average syntactic variables for productive spaces, characterised by a mean depth value of 5.793, RA value of 0.090, and RRA value of 1.126, reflect a low functional efficiency, as detailed in

Table 7. Illustrates the mean depth, RA, RRA, R-value and H* values for the productive and supportive spaces at the architecture school at Salahaddin University-Erbil.

No.	Space Categories		Mean Depth	RA	RRA	H*	R-Value
1	Productive Spaces	Minimum	3.944	0.055	0.692	0.864	1.037
		Maximum	7.861	0.128	1.611
		Mean	5.793	0.090	1.126
2	Supportive Spaces	Minimum	4.769	0.070	0.885	0.906
		Maximum	8.583	0.142	1.781
		Mean	6.682	0.106	1.334
3	Overall	Minimum	3.944	0.055	0.692	0.834
		Maximum	8.583	0.142	1.781
		Mean	6.156	0.096	1.211

. However, specific spaces exhibit a moderate level of functional efficiency. Conversely, the average syntactic variables for supportive spaces, represented by a mean depth value of 6.682, RA value of 0.106, and RRA value of 1.334, are higher than those of productive spaces, signifying a diminished functional efficiency and privacy level within this category. Overall, the average statistical metrics for the entire architectural school spaces are as follows: mean depth value of 6.156, RA value of 0.096, and RRA value of 1.211; these are indicative of a decreased level of functional efficiency-cy within the building.

In addition, it is imperative to consider the varying levels of integration values among the function categories. The mean integration value of the productive spaces—such as design studios, lecture halls, and circulation routes—is 1.126, with a difference factor of 0.864, which signifies a notable degree of differentiation among values, thus indicating a low functional efficiency of this category (Table 7). Conversely, the supportive spaces, comprising administration areas and facilities, exhibit a mean integration value of 1.334, surpassing that of the productive spaces. Nonetheless, the difference factor for this category is weak, at 0.906, implying a marginally lower functional performance com-pared to the productive spaces. The spatial complex, with a mean integration value of 1.211 and a difference factor of 0.834, suggests a low functional efficiency.

Furthermore, the justified-permeability graph for the spaces within building F for the architecture school at Salahaddin University-Erbil has been constructed, as illustrated in Figure 5. There are 109 convex spaces and 113 links representing the accessibility routes among the spaces in the school. Based on these variables, the R-value is 1.037, which indicates the spatial configuration of a tree-structure pattern and points to a low level of functional efficiency among the spaces, as per the justified map. An understanding of this spatial configuration is crucial for optimising space functionality.

To conclude, the syntactical analysis of the spatial configuration in the architecture school at Salahaddin University-Erbil indicates a functional performance within the low to medium range.

4.2. Case Study Two: Architecture School at Cihan University-Erbil

4.2.1. Productive Space Category

The syntactical measurements for the productive spaces dedicated to primary activities exhibit uniformity, which is attributable to the similar spatial configuration of the design studios housed in building no. 9 at Cihan University Erbil. These spaces demonstrate corresponding mean depth (6.548), RA (0.154), and RRA (1.489) values, as delineated in

Table 8. Demonstrates the mean depth, RA, and RRA values for the productive spaces at the architecture school at Cihan University-Erbil. (Source Authors).

Space Category		Space Name	Connectivity	Mean Depth	RA	RRA
Programmed activities	Primary Spaces	Design Studio-No.1 S.F.	1	6.548	0.154	1.489
		Design Studio-No.2 S.F.	1	6.548	0.154	1.489
		Design Studio-No.3 S.F.	1	6.548	0.154	1.489
		Minimum	1	6.548	0.154	1.489
		Maximum	1	6.548	0.154	1.489
		Mean	1	6.548	0.154	1.489
	Secondary Spaces	Lecturer Office No.1 F.F.	1	5.712	0.131	1.264
		Lecturer Office No.2 F.F.	1	4.863	0.107	1.037
		Computer Hall-F.F.	1	4.123	0.087	0.838
		Lecture Hall No.1 F.F.	1	4.534	0.098	0.948
		Lecture Hall No.2 F.F.	1	4.534	0.098	0.948
		Lecture Hall No.3 F. F.	1	4.534	0.098	0.948
		Lecture Hall No.4 F. F.	2	4.534	0.098	0.948
		Lecture Hall No.5 F. F.	1	4.534	0.098	0.948
		Lecture Hall No.6 F.F.	1	4.534	0.098	0.948
		Lecture Hall No.7 F.F.	1	4.534	0.098	0.948
		Lecturer Office No.3 F.F.	1	4.123	0.087	0.838
		Minimum	1	4.123	0.087	0.838
		Maximum	2	5.712	0.131	1.264
		Mean	1.10	4.597	0.100	0.965
Non-programmed activities		Main Entry	3	4.863	0.107	1.037
		Main Reception Hall G.F.	5	4.082	0.086	0.827
		Main Staircase Flight-1 G.F.	3	4.507	0.097	0.941
		Main Staircase Flight-2 G.F.	2	4.027	0.084	0.812
		Main Staircase Flight-3 G.F.	2	4.027	0.084	0.812
		Hall No.2 G.F.	2	4.904	0.108	1.048
		Hall No.1 G.F.	3	5.562	0.127	1.224
		Upper Staircase Flight-1 G.F.	2	5.589	0.127	1.231
		Upper Staircase Flight-2 G.F.	2	4.932	0.109	1.055
		Elevators	3	3.342	0.065	0.629
		Hall No.3 G.F.	3	4.753	0.104	1.007
		Lower Staircase Flight-1 G.F.	2	4.973	0.110	1.066
		Lower Staircase Flight-2 G.F.	2	4.384	0.094	0.908
		Hall No.3 F.F.	11	3.548	0.071	0.684
		Central Main Hall F.F.	10	3.137	0.059	0.573
		Hall No.2 F.F.	2	3.712	0.075	0.728
		Hall No.1 F.F.	4	4.110	0.086	0.834
		Main Staircase Flight-1 F.F.	3	3.795	0.078	0.750
		Hall No.4 F.F.	2	3.986	0.083	0.801
		Hall No.5 F.F.	4	4.726	0.104	1.000
		Hall No.6 F.F.	4	3.877	0.080	0.772
		Lower Staircase Flight-1 F.F.	2	4.137	0.087	0.842
		Lower Staircase Flight-2 F.F.	2	4.425	0.095	0.919
		Main Staircase Flight-2 F.F.	2	4.096	0.086	0.831
		Main Staircase Flight-3 F.F.	2	4.096	0.086	0.831
		Upper Staircase Flight-1 F.F.	2	4.630	0.101	0.974
		Upper Staircase Flight-2 F.F.	2	4.945	0.110	1.059
		Hall no.1 S.F.	4	4.658	0.102	0.981
		Entrance for Design Studio S.F.	4	5.562	0.127	1.224
		Hall No.2 S.F.	2	4.205	0.089	0.860
		Central Main Hall F.F.	5	3.658	0.074	0.713
		Hall No.3 S.F.	3	4.219	0.089	0.864
		Minimum	2	3.137	0.059	0.573
		Maximum	11	5.589	0.127	1.231
		Mean	3.250	4.358	0.093	0.901

. These syntactical values describing the productive spaces for primary activities signify the segregated characteristics and suboptimal functional performance of these spaces. Overall, these spaces rank lowest in functional performance across all space categories.

As the productive spaces for secondary activities, the lecture halls exhibit comparable syntactical values, with a mean depth value of 4534, RA of 0.98, and RRA of 0.948 (Table 8). These values denote integrated properties and a moderate level of functional performance. Notably, certain lecturer offices are segregated and manifest decreased functional performance levels. As a result, it can be deduced that the functional performance within this classification of space is moderate.

According to the data gathered from the analysis, there are variations in the statistical data among the productive spaces for non-programmed activities. Specifically, the central main hall on the first floor exhibits a mean depth value of 3.137, an RA value of 0.059, and an RRA value of 0.573. These values indicate the prevalence of space integration in the building and a high level of functional performance. Furthermore, the average syntactical measurement of spaces in this category reflects the unified nature of the spaces and a moderate level of functional performance.

4.2.2. Supportive-Space Category

The supportive spaces designed for scheduled activities, with an average mean depth value of 6.137, an RA value of 0.143, and an RRA value of 1.378 (

Table 9. Shows the mean depth, RA, and RRA values for supportive spaces in the architecture school at Cihan University-Erbil. (Source: Authors).

Space Category	Space Name	Connectivity	Mean Depth	RA	RRA
Programmed activities	Secretary Room-DAE F.F.	2	5.658	0.129	1.250
	Head of DAE Office F.F.	2	6.616	0.156	1.507
	Minimum	1	4.769	0.070	0.885
	Maximum	6	6.713	0.107	1.342
	Mean	2.33	6.137	0.143	1.378
Non-programmed activities	W.C. Staff Male F.F.	1	7.603	0.183	1.772
	W.C. Staff Female F.F.	3	4.808	0.106	1.022
	W.C. Staff Female F.F.	1	5.795	0.133	1.286
	W.C. Staff Female F.F.	1	5.795	0.133	1.286
	W.C. Student Female F.F.	6	4.397	0.094	0.912
	W.C. Student Female F.F.	1	5.384	0.122	1.176
	W.C. Student Female F.F.	1	5.384	0.122	1.176
	W.C. Student Female F.F.	1	5.384	0.122	1.176
	W.C. Student Female F.F.	1	5.384	0.122	1.176
	W.C. Student Female F.F.	1	5.384	0.122	1.176
	W.C. Student Male F.F.	4	5.014	0.111	1.077
	W.C. Student Male F.F.	1	6.000	0.139	1.342
	W.C. Student Male F.F.	1	6.000	0.139	1.342
	W.C. Student Male F.F.	1	6.000	0.139	1.342
	W.C. Student Male S.F.	6	5.507	0.125	1.209
	W.C. Student Male S.F.	1	6.493	0.153	1.474
	W.C. Student Male S.F.	1	6.493	0.153	1.474
	W.C. Student Male S.F.	1	6.493	0.153	1.474
	W.C. Student Male S.F.	1	6.493	0.153	1.474
	W.C. Student Male S.F.	1	6.493	0.153	1.474
	W.C. Student Female S.F.	6	5.068	0.113	1.092
	W.C. Student Female S.F.	1	6.055	0.140	1.356
	W.C. Student Female S.F.	1	6.055	0.140	1.356
	W.C. Student Female S.F.	1	6.055	0.140	1.356
	W.C. Student Female S.F.	1	6.055	0.140	1.356
	W.C. Student Female S.F.	1	6.055	0.140	1.356
	Minimum	1	4.397	0.094	0.912
	Maximum	6	7.603	0.183	1.772
	Mean	1.769	5.832	0.134	1.297

), show significant segregation and limited functional performance. These statistical indicators, which measure the spatial layout and functional efficiency, also refer to the required level of privacy within these areas.

Similarly, the supportive spaces intended for non-scheduled activities exhibit the highest syntactical values across the building, with an average mean depth value of 5.832, an RA value of 0.134, and an RRA value of 1.297, as shown in Table 9. These measurements comprise the highest levels of segregation and decreased functionality within this specific category of spaces.

4.2.3. Overall Functional Performance of the School

Considering the diverse integration values among the functional categories within the spatial configuration of the architecture school at Cihan University-Erbil is essential. The mean integration value of productive spaces, encompassing design studios, lecture halls, and circulation routes, is calculated to be 0.955, with a difference factor of 0.826, suggesting a notable degree of differentiation among values and thereby indicating a medium functional efficiency for this category (refer to

Table 10. Illustrates the mean depth, RA, RRA, R-value, and H* values for the productive and supportive spaces at the architecture school of Cihan University-Erbil. (Source: Authors).

No.	Space Categories		Mean Depth	RA	RRA	H*	R-Value
1	Productive Spaces	Minimum	3.137	0.059	0.573	0.826	1.108
		Maximum	6.548	0.154	1.489
		Mean	4.558	0.099	0.955
2	Supportive Spaces	Minimum	4.397	0.094	0.912	0.913
		Maximum	7.603	0.183	1.772
		Mean	5.854	0.135	1.302
3	Overall	Minimum	3.137	0.059	0.573	0.768
		Maximum	7.603	0.183	1.772
		Mean	5.049	0.112	1.086

). In contrast, the supportive spaces, consisting of administration areas and facilities, exhibit a higher mean integration value of 1.302, surpassing productive spaces. However, the difference factor for this category is comparatively weaker, at 0.913, implying a marginally lower functional performance compared to the productive spaces. The overall spatial complex boasts a mean integration value of 1.086, with a difference factor of 0.768, indicating an intermediate functional efficiency (Table 10).

In addition, 74 convex spaces and 81 links present the physically accessible routes among spaces in the spatial complex (Figure 6). The R-value for the spaces within the architecture mentioned above stands at 1.108, revealing a ring structure pattern of spatial configuration and pointing to an elevated level of functional efficiency among the spaces, as per the provided map. Comprehending this spatial configuration is integral in optimising the functionality of a space. In conclusion, the syntactical analysis of the spatial configuration at Cihan University’s architecture school in Erbil indicates moderate functional performance, despite the overall integration value of the spatial layouts, which is 1.086.

4.3. Case Study Three: Architecture School at Koya University

4.3.1. Productive Space Category

The design studios within the architecture school share consistent spatial characteristics as productive spaces for primary activities. These studios possess average depth values of 4.746, RA values of 0.114, and RRA values of 1.037, indicating segregated properties and a range of functional performance from low to medium (

Table 11. Demonstrates the mean depth, RA, and RRA values for the productive spaces at the architecture school at Koya University. (Source: Authors).

Space Category		Space Name	Connectivity	Mean Depth	RA	RRA
Programmed activities	Primary Spaces	Design Studio No.01 F.F.	1	4.746	0.114	1.037
		Design Studio No.02 F.F.	1	4.746	0.114	1.037
		Design Studio No.03 F.F.	1	4.746	0.114	1.037
		Design Studio No.04 F.F.	1	4.746	0.114	1.037
		Design Studio No.05 F.F.	1	4.746	0.114	1.037
		Minimum	1	4.746	0.114	1.037
		Maximum	1	4.746	0.114	1.037
		Mean	1	4.746	0.114	1.037
	Secondary Spaces	Lecturer Office No.01	1	6.179	0.157	1.434
		Lecturer Office No.02	1	6.179	0.157	1.434
		Library G.F.	1	5.224	0.128	1.169
		Computer hall F.F.	1	4.418	0.104	0.946
		Lecture Hall No. 08 F.F.	1	4.418	0.104	0.946
		Lecture Hall No. 06 F.F.	1	4.881	0.118	1.074
		Minimum	1	4.418	0.104	0.946
		Maximum	1	6.179	0.157	1.434
		Mean	1	5.216	0.128	1.167
Non-programmed activities		Main Building Entrance	1	6.403	0.164	1.496
		Main Building Reception	2	5.418	0.134	1.223
		Reception Hall No.01 G.F.	5	4.463	0.105	0.959
		Hall No.02 G.F.	3	5.015	0.122	1.112
		Main Staircase Flight-1	2	4.776	0.114	1.045
		Hall No.03 G.F.	3	5.970	0.151	1.376
		Hall No.04 G.F.	2	5.418	0.134	1.223
		Hall No.05 G.F.	5	4.239	0.098	0.897
		Hall No.06 G.F.	3	5.194	0.127	1.161
		Left-Hand Staircase G.F.	2	3.866	0.087	0.793
		Hall No.07 G.F.	4	5.015	0.122	1.112
		Building Courtyard No.01 G.F.	2	5.881	0.148	1.351
		Student Cafeteria F.F.	4	5.716	0.143	1.306
		Shop-G.F.	1	6.701	0.173	1.578
		Staff-Cafeteria G.F.	1	6.701	0.173	1.578
		Hall No.08 G.F.	3	5.806	0.146	1.331
		Building Courtyard No.02 G.F.	2	6.403	0.164	1.496
		Right-Hand Staircase G.F.	2	4.881	0.118	1.074
		Hall No.09 G.F.	3	5.075	0.123	1.128
		Main Staircase Flight-2 G.F.	2	4.433	0.104	0.950
		Main Staircase Flight-3 G.F.	2	4.433	0.104	0.950
		Hall No.01 F.F.	7	4.030	0.092	0.839
		Hall No.02 F.F.	7	3.761	0.084	0.764
		Hall No.03 F.F.	6	3.433	0.074	0.674
		Hall No.04 F.F.	4	3.896	0.088	0.802
		Hall No.05 F.F.	3	4.433	0.104	0.950
		Hall No.06 F.F.	2	4.925	0.119	1.087
		Hall No.07 F.F.	2	5.194	0.127	1.161
		Hall No.08 F.F.	2	4.851	0.117	1.066
		Hall No.09 F.F.	4	4.806	0.115	1.054
		Minimum	1	3.433	0.074	0.674
		Maximum	7	6.701	0.173	1.578
		Mean	3.03	5.038	0.122	1.118

).

Productive spaces for secondary activity reflect a diverse range of syntactical values. Computer Hall F.F. and Lecture Hall No.08 F.F. exhibit similar mean depth (4.418), RA (0.104), and RRA (0.946) values, indicating integrated properties and medium functional efficiency (Table 11). Conversely, the overall average mean depth value (5.126), RA value (0.128), and RRA value (1.167) suggest segregated properties and low functional efficiency within these space categories, thus emphasising the complexity of the spatial analysis.

The spatial analysis data uncover significant disparities among productive spaces for non-programmed activities, underscoring the crucial importance of the varying functional performance levels. Some spaces demonstrate integrated properties and a medium level of functional performance, while others display segregated properties and low functional performance. The average syntactical values for this space category are a mean depth value of 5.038, an RA value of 0.122, and an RRA value of 1.118, signifying segregated properties and low functional performance (Table 11).

4.3.2. Supportive-Space Category

The syntactical measurements for supportive spaces for programmed space reveal segregated properties and low functional performance. The average quantitative measurements for supportive spaces for programmed activities are a mean depth of 5.323, an RA of 0.131, and an RRA of 1.197 (

Table 12. Illustrates the mean depth, RA, and RRA values for supportive spaces in the architecture school at Koya University. (Source: Authors).

Space Category	Space Name	Connectivity	Mean Depth	RA	RRA
Programmed activities	Reporter Office-DAE F.F.	1	5.015	0.122	1.112
	Secretary Office-DAE F.F.	2	4.985	0.121	1.103
	Head of DAE Office F.F.	1	5.970	0.151	1.376
	Minimum	1	4.985	0.121	1.103
	Maximum	2	5.970	0.151	1.376
	Mean	1.33	5.323	0.131	1.197
Non-programmed activities	Store No.01 F.F.	3	5.731	0.143	1.310
	W.C. Staff Male F.F.	1	5.791	0.145	1.326
	W.C. Staff Male F.F.	1	6.716	0.173	1.583
	W.C. Staff Male F.F.	1	6.716	0.173	1.583
	W.C. Staff Female F.F.	1	6.716	0.173	1.583
	W.C. Staff Female F.F.	1	6.716	0.173	1.583
	W.C. Staff Female F.F.	3	5.731	0.143	1.310
	W.C. Student Female F.F.	2	4.179	0.096	0.880
	W.C. Student Female F.F.	2	4.955	0.120	1.095
	W.C. Student Female F.F.	7	5.761	0.144	1.318
	W.C. Student Female F.F.	1	6.746	0.174	1.591
	W.C. Student Female F.F.	1	6.746	0.174	1.591
	W.C. Student Female F.F.	1	6.746	0.174	1.591
	W.C. Student Female F.F.	1	6.746	0.174	1.591
	W.C. Student Female F.F.	1	6.746	0.174	1.591
	W.C. Student Female F.F.	1	6.746	0.174	1.591
	W.C. Student Male F.F.	2	4.642	0.110	1.008
	W.C. Student Male F.F.	2	5.418	0.134	1.223
	W.C. Student Male F.F.	7	6.224	0.158	1.446
	W.C. Student Male F.F.	1	7.209	0.188	1.719
	W.C. Student Male F.F.	1	7.209	0.188	1.719
	W.C. Student Male F.F.	1	7.209	0.188	1.719
	W.C. Student Male F.F.	1	7.209	0.188	1.719
	W.C. Student Male F.F.	1	7.209	0.188	1.719
	W.C. Student Male F.F.	1	7.209	0.188	1.719
	Minimum	1.00	4.179	0.096	0.880
	Maximum	7	7.209	0.188	1.719
	Mean	1.80	6.361	0.162	1.484

), indicating their segregated spatial properties and low functional performance. Contrastingly, the average statistical values for supportive spaces for non-programmed activities include a mean depth value of 6.361, an RA value of 0.162, and an RRA value of 1.484 (as shown in Table 12), underscoring the prevalence of segregated properties and the high degree of privacy within these spaces. These values also highlight the low functional efficiency of these spaces, indicating the lowest functional efficiency level within the space categories.

4.3.3. Overall Functional Performance of the School

Based on the findings, it is evident that the syntactical measurements for productive spaces are notably lower than those for supportive spaces (

Table 13. Illustrates the mean depth, RA, RRA, R-value and H* values for the productive and supportive spaces at the architecture school of Koya University. (Source: Authors).

No.	Space Categories		Mean Depth	RA	RRA	H*	R-Value
1	Productive Spaces	Minimum	3.433	0.074	0.674	0.863	1.115
		Maximum	6.701	0.173	1.578
		Mean	5.028	0.122	1.115
2	Supportive Spaces	Minimum	4.179	0.096	0.880	0.913
		Maximum	7.209	0.188	1.719
		Mean	6.250	0.159	1.453
3	Overall	Minimum	3.433	0.074	0.674	0.839
		Maximum	7.209	0.188	1.719
		Mean	5.524	0.137	1.252

). Nevertheless, the average statistical values for mean depth (5.524), RA (0.137), and RRA (1.252) serve to underscore the segregated nature of the properties and the low functional efficiency inherent within the spaces of the architecture school at Koya University.

It is imperative to analyse the varying degrees of integration value among the different functional areas within the spatial layout of the architecture school at Koya University. The productive spaces’ average integration value, encompassing design studios, lecture halls, and circulation routes, is computed to be 1.115. In conjunction with the difference factor of 0.863, this value indicates significant variability among the values, implying a low functional efficiency within this category (refer to Table 13). Conversely, supportive spaces, such as administration areas and facilities, exhibit a higher average integration value, at 1.453, surpassing the productive spaces. However, the difference factor for this category is weaker, at 0.913, suggesting a slightly lower functional performance compared to the productive spaces. The overall spatial complex has an average integration value of 1.252, with a difference factor of 0.839, signifying low functional efficiency (Table 13).

The diagram presented in Figure 7 delineates the justified graph of the dedicated spaces for architectural education within the College of Engineering building at Koya University. There are 69 convex spaces in the built layout and 77 accessible links between spaces. The R-value for all spaces, a measure of flexibility supporting functional performance, is 1.101, signifying a commendable level of adaptability. This reflects the ring-ness structure of the spatial configuration of the building layout. The R-value assessment underscores the satisfactory level of functional efficiency of the architectural education spaces within the College of Engineering building at Koya University.

In summary, the syntactical analysis of the spatial configuration at Koya University’s architecture school indicates low functional performance. However, the R-value indicates the ring structure of spatial configuration in the spatial complex.

5. Discussion

Several critical issues emerge in interpreting the syntactical values derived from the case studies. First, a comparative analysis reveals that productive spaces’ functional efficiency marginally surpasses that for the supportive spaces, as indicated by the RRA and H* values in

Table 14. Illustrates the summary of syntactical characteristics for all case studies. (Source: Authors).

No.	Space Category		Mean RRA			H*			R-Value
			Case Study-1	Case Study-2	Case Study-3	Case Study-1	Case Study-2	Case Study-3	Case Study-1	Case Study-2	Case Study-3
1	Productive Spaces	Programmed Activities— Primary Spaces	1.175	1.489	1.037	0.864	0.826	0.863	1.037	1.108	1.101
		Programmed Activities— Secondary Spaces	1.205	0.965	1.167
		Non-programmed activity	1.065	0.901	1.118
		Overall Spaces	1.125	0.955	1.115
2	Supportive Spaces	Programmed Activity	1.120	1.378	1.197	0.906	0.913	0.913
		Non-programmed activity	1.427	1.297	1.484
		Overall Spaces	1.33	1.302	1.453
3	Entirety of the Space in the School		1.211	1.086	1.252	0.834	0.768	0.839

. The average integration values observed in the productive spaces of the case studies are as follows: Case Study One: 1.125, Case Study Two: 0.995, and Case Study Three: 1.115. The corresponding mean depths for these case studies are as follows: Case Study One: 5.793, Case Study Two: 4.558, and Case Study Three: 5.028. These results indicate that productive spaces generally feature shallow depths, high flexibility, and enhanced integration. As a result, users encounter fewer steps when transitioning between different areas. In contrast, the average integration values for the supportive spaces were recorded as follows: Case Study One: 1.334, Case Study Two: 1.302, and Case Study Three: 1.453. The respective mean depths for these cases are as follows: Case Study One: 6.682, Case Study Two: 5.854, and Case Study Three: 6.250. These findings suggest that supportive spaces are characterised by greater depths, increased rigidity, and a higher degree of segregation. Consequently, users must navigate more steps to move between various areas within this category. This outcome highlights the utility of a systematic design approach in the analysed case studies. However, optimising the functional performance of both categories of spaces is crucial, as their performance consistently falls short of the established high and medium functional benchmarks across all schools examined, as illustrated in Figure 8. This study suggests that reducing the spatial depth and increasing connectivity among the spaces within the layout, which leads to a lowering of the RRA value to 0.4 or 0.6, are essential steps for significantly enhancing the overall functional effectiveness of the spatial configuration.

Second, the spatial configurations of productive areas, particularly design studios, across all three analysed architecture schools demonstrate suboptimal functional performance indices. High integration values characterised this phenomenon—Case Study One: 1.175, Case Study Two: 1.489, and Case Study Three: 1.370—alongside varying mean depths—Case Study One: 6.003, Case Study Two: 6.548, and Case Study Three: 4.746. These metrics are crucial for assessing the analysed spaces’ depth, rigidity, and segregation-based properties. Additionally, architecture students must navigate five to six areas to reach the design studio. This factor significantly impacts both the frequency of use and the functionality of these environments. It is essential to prioritise the optimisation of studio spaces to improve the effectiveness of architectural education. To achieve this goal, it is crucial to minimise the distance students must travel to access design studios and ensure that the integration value of these spaces remains between 0.4 and 0.6. This strategy aims to enhance functional performance metrics and create a more efficient learning environment. Third, productive spaces allocated for non-programmed activities exhibit the lowest integration values, reflecting satisfactory functional efficiency for these categories, as depicted in Table 14. In contrast, supportive spaces for non-programmed activities, such as W.C. facilities for staff and students, demonstrate high syntactical values. This observation signifies a deliberate incorporation of privacy considerations within the spatial organisation, as outlined in Table 14.

Moreover, functional efficiency assessments indicate moderate performance levels for the architecture school at Cihan University-Erbil (Table 14). This institution features a ring-structured spatial configuration that enhances accessibility and circulation within the built environment. In comparison, Salahaddin University-Erbil displays significantly lower levels of efficiency. The architecture school’s spatial configuration adheres to a tree structure, which presents distinct operational challenges and pedagogical opportunities. This inherent design complexity highlights the necessity for a nuanced and multifaceted approach to the optimisation of functional efficiency within the educational setting. Furthermore, based on the RRA and H* values, Koya University reflects the lowest functional efficiency among the case studies presented (Table 14, Figure 8 and Figure 9). The present study’s findings align with prior research evaluating functional performance levels by applying adopted syntactical space-syntax variables, particularly across diverse spatial layouts [3,5].

The current study has a few limitations. First, the researchers examined the spatial configuration in three architecture schools in Erbil and noted that none of these institutions possesses a dedicated building designed for architectural education facilities. Second, although the research findings provide valuable insights into the functional performance evaluation process, their generalisation is limited. However, examining well-designed architecture schools within various contexts will help recognise the functional performance requirements for each type of space. In addition, the study utilised quantitative data to evaluate the functional performance level in each case study. However, including qualitative data in similar research is essential for bolstering the research’s credibility and enabling a comparison between the quantitative and qualitative data.

Designers and educational administrators can employ this study’s framework, findings, and research design guidelines as part of an evidence-based design approach. Prioritising design studios within architectural school spaces is essential to achieve a more integrated and efficient layout. Additionally, transition spaces in architecture schools, which play a critical role in providing clear visual and physical access to productive areas, should be emphasised. Furthermore, the arrangement of spaces should be based on specific categories and the curricular requirements of architectural education. Using Space Syntax Theory tools and techniques to design and redesign learning spaces within architecture schools can optimise the functional efficiency of these spaces. Moreover, employing the current research methodology to analyse architecture schools in various contexts will be valuable in identifying spatial performance deficiencies and comparing different spatial layouts.

The current research framework makes a unique and significant contribution to interior design, architecture, and education. It provides a comprehensive syntactic description of individual spaces and space categories, offering valuable insights for the design and reconfiguration of learning environments. The study’s outcomes are crucial for evaluating and improving the functional efficiency of architecture schools, particularly in similar educational built environments.

6. Conclusions

Space Syntax Theory has been extensively applied to the analysis of higher-education environments, with particular emphasis on university campus design, focusing on pedestrian circulation patterns, contextual integration, and sustainability metrics. This theoretical framework has been instrumental in examining the intricate relationships between the spatial configurations of learning environments and their impacts on pedagogical experiences, social interactions, circulatory efficiency, and overall functional performance. The present study employed a comprehensive set of syntactical parameters—including mean depth, RA, RRA, H*, and R-value—to evaluate the functional efficiency of three architecture schools located in Erbil. The methodological approach incorporated axial-map analysis and justified graphs to elucidate the spatial complexities inherent in the case studies.

The findings reveal significant variations in functional efficiency across the institutions examined. The architecture school at Cihan University-Erbil demonstrated moderate functional efficiency, characterised by a ring-structure spatial configuration that facilitates enhanced accessibility and circulation within the built environment. In contrast, the architecture schools at Salahaddin University-Erbil and Koya University exhibited lower levels of functional efficiency, with the latter featuring a tree-structure spatial configuration that constrains inter-space accessibility.

The framework, findings, and guidelines outlined in this study provide designers and educational administrators with a foundation for employing evidence-based strategies to enhance the spatial designs of architectural schools. Key considerations include the strategic prioritisation of design studios, the optimisation of transition spaces to ensure seamless accessibility, and the organisation of spatial layouts in alignment with the curricular demands of architectural education, fostering a cohesive and effective learning environment. In contrast, this study is limited to three architecture schools in Erbil, none of which have buildings exclusively used for architectural education, and its findings have limited generalizability. The use of qualitative data in future research could enhance credibility and provide a more comprehensive analysis of functional performance across diverse contexts. Examining well-designed architecture schools in diverse contexts could further refine the understanding of functional performance requirements for different spaces.

This research framework contributes substantially to interior design, architecture, and education by providing empirically grounded insights into the design and reconfiguration of learning environments. However, further investigation incorporating qualitative methodologies and a broader sample of dedicated architectural education facilities is recommended to enhance the robustness and generalizability of these findings.