# Introduction & History

Space syntax, or the syntactical analysis of spatial data and networks, is a technique in urban geographical and geospatial sciences which marries real-world use of spaces and networks with underlying graph theory. The techniques were originally developed by Hillier & Hanson at the University college of London in the 1970s[1]. At a glance, urban space looks and feels continuous in nature, particularly when navigating it as a pedestrian - humans do not navigate their surroundings in terms of rigid distinctions between nodes and edges or ways, but rather as cohesive paths. Further, network-rigid analysis typically casts the differences between nodes in units of metric distance, whereas human behavior is often governed by more complex relationships between spaces; cognitive and visual spaces are topological in nature, and human behavior is more influenced by local relatives than global metrics[2]. We will later see that space syntax modeling accounts for this preference towards non-distance-metric relationships between spaces; space syntax, simply, models human behavior by discretizing the urban fabric through which users may move.

It can be easy to take the structure of a given network as static, constant, and unchanging - however, human behavior shapes and molds urban fabric over time, and in turn the relationships both between spaces and people change. In this way, both society (human behavior) and urban space are dynamic and serve to modify each other, as opposed to humans simply behaving on top of a pre-existing layer of unchanging networks[3]. Space syntax can analyze these changes over time, as the relative importance of places is related to the surrounding network structure - and network structure is frequently altered via human behavior; when the importance of a place changes, human behavior is affected. Space syntax modeling can help determine why exactly a place is important to people through metrics that don't pertain to distance between places - rather, metrics of the surrounding network both locally and globally can be calculated and used to predict user behavior.

Relative comparisons between networks are also very important, particularly when considering transportation mode-shares, network structures, and human behavior among networks of different absolute spatial sizes. By removing the factor of absolute distance between two points on a network, an element of scale is removed which can restrict the validity of comparison between different networks. Space syntax modeling allows for topological abstraction, that is, reducing a network down to its most salient properties (what is connected to what), and eliminating superfluous or unnecessary levels of detail (precise distance metrics, minor differences in built environment characteristics). While levels of granularity are indeed lost in the abstraction, the power of network structure comparison is gained, allowing for categorization of networks on typological terms[3].

Space syntax techniques are frequently used throughout Europe and Asia in urban planning and analysis, but are significantly underutilized in the United States[4]. As we will see, such techniques can immediately bring to light the relationships between human behavior and different orientations and organizations of space and networks.

# Theory & Terminology

The basis of space syntax analysis is the construction of a graph (or graphs), and the calculation of various metrics on the graph(s). Beginning abstractly, a convex map of an area is created as the set of fewest large convex spaces, given any boundary constraints. Then, an "axial map" is constructed from the set of all longest axes that connect all convex subspaces - this is typically done in an iterative manner, starting with the longest axial line. And finally, a network graph is constructed, where each axial line from the axial map is a node in the graph, and the intersections of the axial lines in the map are represented by connections (edges) in the network graph[5]. Figure 1 in Bafna (2003) shows a basic mapping of an office schematic to a graph first for a single hallway topology, and then with two parallel hallways. This will later help illustrate the space syntax metric of control.

Figure 2 in Bafna (2003) shows the importance of dividing non-convex spaces into sets of convex spaces when creating axial graphs, as well as the power of space syntax to easily illustrate spatial hierarchy. Axial graphs typically follow a "line of sight" principle, in that in order to reach an adjacent node from a starting node, one must be able to see the destination.In its strictest sense, this dictates that roads that have curves must be modeled as discretizations among many segments, with dummy nodes at corners, but this is not necessarily always the case. First proposed by Figueiredo and Amorim, a maximum angle of continuity can be defined as the angle beyond which a link must be subdivided at a turn[6]. By constructing a "reverse" graph, where road or pedestrian links are nodes, and their intersections are edges, the space syntax approach emphasizes transitions between spaces in which traversing the network graph means taking turns on the geographical map, and discounts the length of spatial links [5]. Analytic metrics are then calculated on this reversed network graph. Figure 1 in McCahil & Garrick (2008) illustrates the construction of axial maps and reversed network graphs in the space syntax framework. Here it is easy to see how the nodes and edges in the constructed network graph correspond to road links and intersections in the geographical and axial maps.

Following is a list of terms and analytical metrics used in the space syntax framework:

• Network depth: defined as the fewest number of vertices connecting any two nodes. Translated from the space syntax network graph to an actual network, this is the fewest number of roads or links connecting any two different roads or links.
• Mean depth: the total depth of a node divided by the total number of nodes.
• Integration: also known as relative asymmetry, describes how easily accessible a given node is from other nodes in the system. ${\displaystyle I=2(MD-1)/(k-2)}$  is an example of how integration can be calculated for a network, where MD is mean depth as above and k is the number of nodes [4].
• Betweenness: a form of centrality, describes how "between" a place is among other places - that is, how often a place is traversed when traveling between other origins and destinations.
• Angular segment analysis: a modification of the original space syntax methodology which addressed the variable values and costs of turns by angle.
• Connectivity: a measure of how well a given place is connected to surrounding nodes; also, the number of links connecting into a given link. Better-connected places have higher in-degree and out-degree, and typically have lower depths from other nodes.
• Intelligibility: particularly in human behavior and spatial psychology, measures the ease with which a user may navigate and orient within a space.
• Asymmetry: a difference in depth, or connectivity, between two places will produce a comparative asymmetry in hierarchy or importance of a place.
• Rings: the presence of rings in a network will serve to reduce control and hierarchy, as well as mean depth.
• Chains:the presence of chains in a network will serve to increase control and hierarchy, mean depth, and decrease the integration.

Integration describes how well integrated, or enmeshed, a place is within a network, and higher integration correlates with lower nodal depth (it takes fewer moves to reach the node from other nodes). However, integration measures concentrate on the attractiveness of a destination, and not on route choice either to or through a place. In contrast to integration measures, betweenness centrality metrics account for route choice behavior, and give a picture of the importance of links not just surrounding origins and destinations, but also in the middle of route trees. Betweenness centrality is a popular measure, and is the metric of choice for several of the case studies listed below[5].

It is worth noting that the original space syntax framework lumped all turns together when constructing axial maps - i.e. that all bends in roadways were treated equally regardless of angle, resulting in uniform trip cost effects from turning. Angular segment analysis, described above, modified the framework to assign lower costs to shallower turns, and higher costs to more acute-angle turns[7]. This allows for a much more fluid and realistic representation of road networks in the space syntax framework, with fewer significant changes in topological orientation. Moreover, the use of angular analysis allows one to use road centerline maps, which are often readily available, as approximate axial maps; this is due to the more realistic topology of axial maps created with progressive turn-penalizing angular analysis[7][8].

# Case Studies

## Walking in New Urbanist and Suburban Neighborhoods

Space syntax analysis can also very clearly illustrate how characteristic changes and differences in urban form affect human walking behavior. Intuitively, we know that a network or space that is less pedestrian friendly will probably have a lower mode-share for walking, and will experience lower walking trip generation for leisure or commute purposes. However, space syntax network analysis can quantify walking trip generation in terms of the underlying network characteristics. This study by Baran et al. (2008) looks at walking behavior and how it changes between a new urbanist community and a suburban community, and evaluates the physical environment differences using space syntax analysis. The syntactical variables analysed here are control, local integration, and global integration, and are assessed in terms of their explanatory power for both leisure and utilitarian walking in new urbanist and suburban environments[9].

Figures 1 through 4 show the variance of syntatic variables control, local integration, and global integration, for the new urbanist community. Overall, it's readily seen that there are not many completely unconnected links (dead ends), and a less stratified hierarchy of links and roads exists. The highest control roads in a network are those that would break the most connections were it to be out of service, and those with lowest control are roads with no consequence to going out of service. Points of local and global integration maxima may differ, depending on the importance to integration of links beyond the cutoff threshold. And in the axial map of the suburban community, it is readily apparent that a large number of links are highly segregated and/or stratified, and the network is very tree-like.

 Figure 1: displays the variance of syntatic variable "control" in new urbanist community. Figure 2: displays variance of syntatic variable "local integration" in new urbanist community.
 Figure 3: displays variance of syntatic variable "global integration" in new urbanist community. Figure 4: displays variance of syntatic variable "global integration" in suburban community.

The authors found positive relationships between walking and mean global integration (significant at p < 0.01), and mean local integration (significant at p < 0.01). Mean control was not found to be significantly correlated with walking. Mean variable coefficients were higher in the new urbanist neighborhood for local and global integration. Axial line lengths were typically much lower in the new urbanist neighborhood than suburban neighborhoods.

## Cyclist Route Choice in London

Route choice is a common application of the space syntax framework, as by its nature it predicts the most highly used link segments in a network. When determining a likely route from an origin to destination, higher probabilities of link usage can be assigned to links determined to be more important in the space syntax analysis. Additionally, route choice is especially important for modes highly susceptible to safety and continuity factors, such as bicycles. Figure 1 in Raford, Chiaradia, and Gil shows the study areas in London, including areas both north and south of the River Thames[10]. The authors analyzed two separate datasets to test for saliency and explanatory power in the space syntax metrics for the London street network - a sample of 423 cyclist trip diaries to test for important factors on an individual-cyclist basis, and aggregate cyclist volumes in select areas in London.

Figure 5 in Raford, Chiaradia, and Gil shows the type of overlay analysis conducted for individual bicycle trips, to test if space syntax metrics were relevant to route choice on an individual basis. Individual trips were found to be exceedingly hard to predict, and route choice on the individual trip level did not correlate well with the shortest path or fastest cognitive route (angular minimization), in that neither factor was solely important in actual cyclist route choice. However, aggregating cyclist behavior to a population level allows emergent properties to appear[10]. If a particular road segment is friendly to bicycles, an individual cyclist may or may not take that segment depending on origin and destination, among other factors, but in aggregate a population of cyclists will show heavier use on more important routes. Indeed, this was found to be true - global mean angular depth, a statistic of space syntax analysis, correlated well to cyclist counts.

## Bicycle Facility Planning in Cambridge, MA

The relationship between space syntax analytical framework and techniques, and analysis of bicycle facilities, was investigated in Cambridge, MA by McCahil & Garrick (2008)[5]. This represents another practical and salient example to illustrate the power of space syntax modeling to assess a transportation network on the basis of its emergent travel patterns for different network configurations. As space syntax itself is devoid of dependence on the characteristics of the built environment, and solely depends on network characteristics, modal travel demand modeling can be performed without extensive and tedious origin-destination studies. McCahil & Garrick modeled bicyclist behavior in Cambridge, MA using the space syntax "choice" parameter (whether a route will include a given road segment).As can be seen in Figure 4 in McCahil & Garrick (2008), the space syntax framework predicted high importance (choice parameter) at many locations which in actuality did experience high bicycle traffic volume from counts.

In the multilayer model constructed to explain bicycle traffic, the authors included population and worker densities as proxies for origin and destination generators, respectively, in addition to the space syntax metrics. They found that the population and worker densities explained a large portion of the cyclist volume data collected, whereas the salience of the space syntax measures was considerably lower in explanatory power. The authors cited the types of bicycle counts that were used as a factor in why the space syntax measures failed to more fully explain the counts, including having to extrapolate link (or "gate") counts from intersection counts. Intersection counts, particularly for bicycles where certain routes may be considerably safer and better developed, fail to exhibit granularity at the link level, which is where space syntax operates.

# Limitations

Space syntax analysis can be a very powerful tool to predict network use and user behavior, as it solely relies on the underlying network structure and it is unnecessary to perform extensive origin-destination trip studies. Such an approach is scalable, and provides results easily compared between different, but categorically similar, urban areas through its removal of distance-based metrics. Space syntax analysis helps predict user behavior without involving considerations of the built environment[2]; however, not considering elements of the built environment in evaluating saliency for pedestrian traffic is also one of the methodology's weaknesses[11]. Space syntax doesn't consider the shapes of open spaces - which are outlined in part by the shapes of surrounding buildings - in considering whether a pedestrian would want to walk there. "Isovists" are convex spaces representing the entire sub-space of a space which an observer may view from a static position. The sizes, shapes, and configurations of isovists are very important in terms of the experience and enjoyment of a space for a user, and again, space syntax does not consider these details.

Space syntax itself may not consider elements of the built environment, but when its network statistics are used in conjunction with built environment elements and, in the case of pedestrians and bicyclists, on-road improvements, a powerful model with much predictive power can be achieved.

# References

1. Hillier, B., and J. Hanson. "The Social Logic of Space." Cambridge University Press, Cambridge, United Kingdom, 1984.
2. a b Penn, A. "Space Syntax and Spatial Cognition, Or Why the Axial Line?. Environment and Behavior, Vol. 35 No.1, January 2003. 30-65.
3. a b Bafna, S. "Space Syntax: A Brief Introduction to its Logic and Analytical Techniques." Environment and Behavior, Vol. 35 No.1, January 2003. 17-29
4. a b Raford, N., and Ragland, D. "Space Syntax: Innovative Pedestrian Volume Modeling Tool for Pedestrian Safety." Transportation Research Record: Journal of the Transportation Research Board, No. 1878, TRB, National Research Council, Washington, D.C., 2004, pp. 66–74.
5. a b c d McCahill, C. and Garrick, N. W. "The Applicability of Space Syntax to Bicycle Facility Planning." Transportation Research Record: Journal of the Transportation Research Board, No. 2074. Transportation Research Board of the National Academies, Washington, D.C., 2008, pp. 46–51.
6. Figueiredo, L., and L. Amorim. Continuity Lines in the Axial System. Proc., Fifth Space Syntax International.
7. a b (Turner, A. Could a Road-Centre Line be an Axial Line in Disguise? Proc., Fifth Space Syntax International Symposium, Delft University of Technology, Delft, Netherlands, 2005.
8. Dalton, N. S. C., J. Peponis, and R. C. Dalton. To Tame a TIGER One Has to Know Its Nature: Extending Weighted Angular Integration Analysis to the Description of GIS Road-Centerline Data for Large Scale Urban Analysis. Proc., Fourth Space Syntax International Symposium, London, 2003.
9. Baran, P. K., Rodríguez, D. A., & Khattak, A. J. (2008). "Space Syntax and Walking in a New Urbanist and Suburban Neighbourhoods." Journal of Urban Design, 13:1, 5-28
10. a b Raford, N., Chiaradia, A., Jorge, G. "Space Syntax: The Role of Urban Form in Cyclist Route Choice in Central London." Presented at 86th Annual Meeting of the Transportation Research Board, Washington, D.C., 2007.
11. Montello, D. R. "The Contribution of Space Syntax to a Comprehensive Theory of Environmental Psychology." Proc. 6th International Space Syntax Symposium, Istanbul, 2007.