## 3 Methods
### Analytical Formula  
[PERSON] (1996) defined a spatial system's \"configuration\" as the degree of relationships that it allows among and through its elements [7]. Space syntax, a methodology developed by [PERSON] and [PERSON] (1984), is a set of analytical techniques used to describe and quantify spatial configurations in cities or buildings, for purposes of urban and architectural planning [8]. [PERSON] and [PERSON] (2005) measured the correlation between measurements of space syntax and pedestrian traffic to identify, from a geometric and topological perspective, how the spatial configuration of street networks influences the movement flows of cities, thus affecting the evolution of land-use patterns [30]. Additionally, [PERSON] and [PERSON] (2016) showed that spatial configuration influences social activities by examining the importance of the configuration related to urban morphology and social relations [31]. Figure 1: The district selected as the research area, containing Yukgeori Market and its vicinity. According to the basic space syntax theory, the mean depth (_MD_) for a space in a system can be calculated by dividing the total depth--the sum of the depths via each of the shortest routes between one space and all other spaces--by the number of spaces in the system. The formula is as follows:  
\[MD_{x}=\frac{\sum_{i\in s,j\
eq x}D(x,i)}{k-1} \tag{1}\]  
where _MD\({}_{x}\)_ is the mean depth of a space \(x\) in system \(S\), _D_(_x,i_) is the depth of the shortest path between space \(x\) and space \(i\) in the system and \(k\) indicates the number of spaces in the system. _MD_ is a measure of the degree of integration/segregation of space in system \(S\); a lower _MD_ for a space means that the space is more integrated into the system. In terms of space syntax, a more integrated space is generally interpreted as a more public space. Angular Segment Analysis (ASA) [32], an analysis model extended from basic space syntax, calculates _MD_ for a space by considering the turning angles from a space to another space as follows:  
\[MD_{x}=\frac{\sum_{i\in s,j\
eq x}D_{\theta}(x,i)}{k-1} \tag{2}\]  
where _D\({}_{\theta}\) (x,i)_ is the depth calculated by considering the angle (\(\theta\)) for each turn from space \(x\) (root) to space \(i\) (destination) in system \(S\), which ranges from 0 (no turn) to 2 (a 180\({}^{\circ}\) turn). In this way, ASA supplements the _MD_ of the basic space syntax mentioned above, which focuses only on topology. This study employed this equation to analyze the city-level research area. The equation was implemented in a computing environment using \"Depthmap X\", an analysis tool developed by [PERSON] (2013) [33]. [PERSON] (2013) understood a city as a network and system of flows, not just as a place. From this perspective, [PERSON] developed methods to capture and express the vast complexity of a city, accounting for streets as nodes and streets as links in a street network [9]. [PERSON] and [PERSON] (2002) suggested the concept of point-based space syntax to model large-scale urban spaces as a finite set of small-scale spaces [34]. The point-based method can analyze urban spaces at a micro level (neighborhood level), while the line-based analysis based on Equations (1) and (2) can analyze the spaces at a macroscopic level (city-level). [PERSON] and [PERSON] (2016) proposed an extended equation for point-based angular analysis, inspired by the concept of point-based space syntax, to identify the attributes of the nodes as a set of points in spaces connected by the path segments in a street network, which cannot be covered by the line-based analysis [35].