## Abstract

This study focused on the structure and the platform of the road space of historic districts. We analyzed the road networks of 16 historic districts in Japan from the perspectives of circularity, accessibility and indirection based on graph theory. By calculating and comparing the indexes of each road network (NW1 and NW2) forms, we quantitatively describe the effects of the main prefectural roads (more than 4 m in width) and narrow streets (less than 4 m in width) on the spatial characteristics. And it turned out that we could divided the 16 objective historic districts into 4 types. Moreover, we qualitatively studied the characteristics of each type of historic districts based on their development background and the structure of road network.

## Keywords

Road network forms ; Historic districts ; Graph theory ; Circularity ; Accessibility

## 1. Introduction

Many cities and villages in Japan have a long history. The spatial form of these historic districts has changed with the progression of urbanization, but many such districts and villages still apply old road networks as spatial frameworks. These frameworks contain not only old streets that serve as the main prefectural roads but also winding narrow alleys that are less than 4 m wide. Although traffic capacities vary, these streets complement one another and jointly constitute the road network form that fits the local lifestyle while maintaining the uniqueness of the area. People wandering in these historic districts are often fascinated by the sequence landscape along the road and the rich variations in the road itself. Thus, these historic streets must be preserved in merging modern urban design with the characteristics of the local area.

Since Japan established the Important Preservation Districts for Groups of Traditional Buildings in 1975, an active movement has been initiated to protect and re-develop historic districts throughout the country. Given the sub-optimal awareness regarding the spatial structure of historic districts in preparing local development plans, many old streets were modified after being regarded as unfavorable factors that impede traffic. As a result, the road network in some originally unique historic districts changed and a few historical surroundings were demolished. Apart from recognizing the importance of historic streets from the perspectives of landscape and culture, the features of spatial structures must be interpreted objectively to avoid conflicts between the re-development of historic districts and the preservation of the historic environment.

On the basis of the afore mentioned viewpoints, 16 historic districts of various formation backgrounds in Japan were taken as examples in this study to analyze the circularity, accessibility, and indirection of the road network individually. This procedure can help quantitatively clarify the features of the road network form in these districts and explore the relationship between road formation and spatial characteristics further.

## 2. Previous studies

To date, researchers in many disciplines have studied the spatial features of historic roads in Japan. In geographic research, for example, historic streets in Japan were classified according to natural and artificial road formation conditions, and the relationship between the characteristics of road sections and the use of land along the road was identified (Rin et al., 1995 ; Kamae et al., 1995 ). In landscape-related studies, the roles of the historic roads in the area within the sequence landscape were explored by analyzing the shapes and angles of the roads and of the surrounding physical environment (Iwakuma, 1997  ;  Miyawaki, 2012 ; Kawakami et al., 2012 ). In papers discussing local communities, the influence of road spatial features in various scales on the communication behavior within the neighborhood inside blocks was determined through field investigations into the environment of historic roads in Kyoto and the functions of the buildings along the roads (Okada and Miyazaki, 2012 ).

The results from the afore mentioned studies indicate that historic road space plays an important role in the formation of local communities and in the continued implementation of urban characteristics in Japan. However, most previous works described the physical characteristics of road spaces from their respective viewpoints. Moreover, research on the overall composition and potential non-visual characteristics of historic road networks in Japan remains scarce.

In studies that examine the re-development of historic regions, many historic districts may emphasize accessibility and circularity; researchers argue that some old streets are highly circuitous and thus contribute little to traffic (Kozuka et al ., 2005  ; Shimizu and Ono, 2006  ;  Aoki et al ., 2010 ). Hence, proposals to demolish and change original road network structures have been presented. However, problems regarding the exact situation of the original road network and the extent to which certain roads affect the overall characteristics of the area are rarely addressed objectively (Tanaka and Akasaki, 2000  ;  Nishiguchi, 2004 ).

In the current study, we focus on the structure and the platform of the road space. Furthermore, we analyze the spatial characteristics of the road networks in historic districts with different formation backgrounds in terms of three aspects that have attracted much attention in regional development, namely, circularity, accessibility, and indirection (Punnoi et al ., 2010  ;  Miyashita et al ., 2013 ). This analysis can help quantitatively illustrate the spatial characteristics and the status quo of the historic roads. This study also presents methods and basic data to effectively recognize road space for coordinating future development plans related to historic regions (Fig. 1 ).

 Fig. 1. The basic information of the research areas.

## 3. Research method

### 3.1. Indicators

In this study, the circularity, accessibility, and indirection of road networks are defined based on graph theory (Watanabe et al., 1983 ). The selected indicators that can be used to quantitatively describe the geometric features of these aspects are listed in Table 1 .

Table 1. Indices of network analysis.
Categories Indices Formula Notes
Circularity Cyclomatic number: µ µ =eν +p e : Number of links ν : Number of nodes P : Number of component
Average Cyclomatic number: µa (n/ha) µa =µ /S S : Area
α -index (%) α=µ /(2ν −5) In copmplete connected network, µc =2ν −5 Ratio of µ /µc
β -index β =e /ν Average number of pass per node
γ -index (%) γ =e /3(ν −2) In copmplete connected network, ec =3(ν −2) Ratio of e /ec
Accessibility Average accessibility: Ai ${\textstyle {\overline {Ai}}={\frac {{\Sigma }_{j=1}^{n}d(i,j)}{\left(n-1\right)}}}$ Average minimum distance from all nodes to node i , d (i ,j ): minimum distance of inter nodes
Average dispersion: Di ${\textstyle Di=\sum _{l=1}^{\nu }\sum _{j=1}^{\nu }d\left(i,j\right)/\nu (\nu -}$${\displaystyle 1)}$ Excepted effect of number of nodes from sum of Ai
Road density: Dl (m/ha) Dl =L /S L : Total length S : Area
Node density: Dc (n/ha) Dc =νc /S νc : Number of intersection S : Area
Indirection Detour ratio A ${\textstyle {\overline {A}}{'}={\frac {{\Sigma }_{j=1}^{n}{\frac {d}{dl}}(i,j)}{\left(n-1\right)}}}$ Average ratio of minimum distance to straight-line distance from all nodes to node i , d (i ,j )
Average detour ratio A ${\textstyle A=\sum _{l=1}^{\nu }\sum _{j=1}^{\nu }{\frac {d}{dl}}\left(i,j\right)/\nu (\nu -}$${\displaystyle 1)}$ Average ratio of minimum distance to straight-line distance of inter network

 Fig. 2. Road network form of research area (Relationship between numbers of links and nodes).

Second, Ai , which is the average of the minimum distances between any given nodes to any other nodes in the graph, is used to assess the accessibility of a given no debased on the concept of distance (Graham et al., 1977 ). In addition, Di , which is the average of the Ai values of all the nodes, is applied to assess the accessibility of the overall road network. Therefore, the smaller the value of Di is, the shorter the relative distance required for the wanderers in the road network to reach each of the nodes and the better the accessibility of the overall road network. A few studies have indicated that the extent and densities of the nodes and links in the network graphs are directly related to the Di indicator ( Koshizuka, 1978  ;  Takagi et al ., 1991 ). In the present study, road network density (Dl ) and node density (Dc ) are utilized to jointly evaluate road network accessibility.

Finally, indirection is defined as the ratio of the actual distance from a certain node to any of the other nodes to the linear distance between the two nodes in the graph. Detour rate (A ) is applied to represent the extent of overall road network indirection ( Tamura et al., 2001 ). The higher the detour rate is, the stronger the indirection of the road network is, i.e., the more circuitous a path a person must take to reach a given node.

### 3.2. Research area

Sixteen villages and city blocks whose historic roads have been well preserved were selected as the objects of analysis based on the following three criteria. The location and features of each district are shown in Fig. 1 .

• Taking into account the effect of the formation background of the historic district on the form of its road network, representative districts were selected. These districts range from traditional villages that rely on agriculture, forestry, and fishery to historic city blocks that depend on industrial or religious facilities.
• In consideration of the effects of geographical conditions, the subjects included relatively independent areas located in between the island and mountain and areas situated in or are close to cities.
• To minimize the influence of modern roads on the form of the historic road network as much as possible, the appropriate subjects were selected as follows: (1) villages with well-preserved original road networks that remain in use based on historical records and local archives; (2) areas that are close to cities but are only slightly affected by urbanization, with most of the road network remaining unchanged; and (3) areas that belong to the Important Preservation Districts for Groups of Traditional Buildings and the city blocks that maintain their original historic road form.

According to the general method of graph theory and considering the different actual road formations of each of the subjects, four rules were set to generate a road network for each of the subjects (Fig. 3 b).

• First, the range of graphs for national or local historical preservation districts is based on the boundary lines that are clearly marked on the city plan. Second, the range of the boundary lines in naturally formed traditional villages is wide given the inclusion of mountain areas and farmland. To compare the subjects at a similar scale, the major residence areas of the traditional villages with relatively densely populated roads were selected to represent the graphing range of the road network.
• Considering that the types of roads within the road network differ and thus exert varied influences on the characteristics of the overall form (Yamazaki et al., 2013 ), the road network structure was divided into main prefectural roads (more than 4 m wide) and narrow streets (less than 4 m wide) based on the information reflected in the 1/2500 Residential Map of Japan. Accordingly, the relationship between road formation and each of the spatial characteristics was clarified. The main prefectural road network (NW1) and the narrow streets in the entire road network (NW2) were analyzed individually (Fig. 3 a).
• The plane forms of the road in this study are divided into straight lines, tortuous lines, and curves. A road that has a low extent of tortuousness has a straight line form if the two ends of the road can be linked by one straight line within the width of the road.
• In Fig. 3 , the terminal node (no link at the other end) of each line is represented by

, and the intersection node is represented by •.

 Fig. 3. (a) The type of road network (Take 14. Chikugoyoshii for example). (b) Road network in the research areas.

## 4. Result and analysis

### 4.1. Circularity characteristics

Table 2. Road network analysis result.
Type NO. Name of historic district Road length (m ) Network1 (The main prefectural road network)
Total length Main Road (>4  m) Narrow Street (<4  m) e ν Number of end point Number of intersection µ µa α (%) β γ (%) Di (m) Dl (m/ha) Dc A
Type1 4 Shiramine 3725 2418 1307 78 74 0 10 5 0.5 3 1.1 36 347 226 0.9 1.3
13 Iwaishima 6311 2599 3711 71 70 1 7 2 0.1 1 1.0 35 515 146 0.4 1.6
16 Taketomi Island 7914 4546 3368 94 78 0 30 17 0.4 11 1.2 41 474 119 0.8 1.3
10 Okikamuro 2857 1565 1293 45 43 1 8 3 0.2 4 1.0 37 252 109 0.6 1.2
11 The West of Higunto 5861 2854 3007 77 75 2 11 3 0.1 2 1.0 35 527 123 0.5 1.3
12 The East of Higunto 7867 3965 3902 110 107 0 14 4 0.2 2 1.0 35 697 150 0.5 1.7
Type2 3 Kuroshima district 3993 2144 1849 53 50 0 9 4 0.2 4 1.1 37 339 105 0.4 1.5
5 Obama-nishigumi 3656 2502 1154 43 39 1 12 5 0.3 7 1.1 39 384 131 0.6 1.3
8 Mitarai 4124 2236 1889 56 51 1 13 6 0.9 6 1.1 38 306 324 1.9 1.4
9 Miyajima 9424 7181 2243 216 198 0 36 19 0.5 5 1.1 37 738 183 0.9 1.7
Type3 1 Motomachi·Suehirocho 6572 6361 212 74 51 0 37 24 1.7 25 1.5 50 430 439 2.6 1.2
2 Makabe 4608 4245 363 49 37 0 23 13 0.7 19 1.3 47 350 241 1.3 1.2
14 Chikugoyoshii 6835 5207 1628 76 61 0 30 16 0.8 14 1.2 43 428 252 1.4 1.3
15 Yamefukushima 5697 4428 1269 51 41 0 20 11 0.6 14 1.2 44 474 224 1.0 1.3
Type4 6 Imai-cho 6820 4929 1891 73 61 0 27 13 0.7 11 1.2 41 400 283 1.6 2.3
7 Tondabayashi 4036 2757 1279 45 36 0 19 10 0.9 15 1.3 44 259 246 1.7 1.4
Type NO. Name of historic district Road length (m ) Network2 (The whole road network)
Total length Main Road (>4  m) Narrow Street (<4  m) e ν Number of end point Number of intersection µ µa α (%) β γ (%) Di (m) Dl (m/ha) Dc A
Type1 4 Shiramine 3725 2418 1307 169 150 10 47 20 1.9 7 1.1 38 336 348 4.4 1.3
13 Iwaishima 6311 2599 3711 257 215 13 87 43 2.4 10 1.2 40 323 355 4.9 1.4
16 Taketomi Island 7914 4546 3368 191 149 5 78 43 1.1 15 1.3 43 456 207 2.0 1.2
10 Okikamuro 2857 1565 1293 105 99 13 28 7 0.5 4 1.1 36 274 198 1.9 1.4
11 The West of Higunto 5861 2854 3007 245 215 22 75 31 1.3 7 1.1 38 461 253 3.2 1.2
12 The East of Higunto 7867 3965 3902 311 278 34 102 34 1.3 6 1.1 38 639 297 3.8 1.4
Type2 3 Kuroshima district 3993 2144 1849 153 127 6 57 27 1.3 11 1.2 41 281 195 2.8 1.3
5 Obama-nishigumi 3656 2502 1154 81 68 6 32 14 0.7 11 1.2 41 339 191 1.7 1.3
8 Mitarai 4124 2236 1889 177 148 17 65 30 4.3 10 1.2 40 242 598 9.4 1.3
9 Miyajima 9424 7181 2243 318 280 12 81 39 1.0 7 1.1 38 571 240 2.1 1.4
Type3 1 Motomachi·Suehirocho 6572 6361 212 86 63 6 43 24 1.7 20 1.4 47 417 453 3.0 1.3
2 Makabe 4608 4245 363 63 49 4 31 15 0.9 16 1.3 45 353 262 1.8 1.3
14 Chikugoyoshii 6835 5207 1628 143 114 2 57 30 1.4 13 1.3 43 406 330 2.8 1.6
15 Yamefukushima 5697 4428 1269 96 77 6 41 20 1.0 13 1.2 43 425 288 2.1 1.3
Type4 6 Imai-cho 6820 4929 1891 135 91 0 66 45 2.6 25 1.5 51 315 392 3.8 1.7
7 Tondabayashi 4036 2757 1279 96 66 0 43 31 2.8 24 1.5 50 253 360 3.8 1.3

 Fig. 4. Cyclomatic number (µ ) and Average Cyclomatic number (µa ).

 Fig. 5. α -index.

On the contrary, 6.Imai-cho and 7.Tondabayashi are “Jinai-cho” towns that were independent settlements formed with temples at the center. The areas surrounding the towns are enclosed by trenches or high walls, and the town is isolated (Horiuchi et al., 2006 ). The road layout is depicted in Fig. 3 . Theintegration of internal transport was emphasized, and the “grid-type” road network form was jointly formed by the roads that were more and less than 4 m wide. Therefore, the number of circular roads is significantly higher in NW2 than inNW1; moreover, the former is more complete in form than the latter. The α value also increases.

 Fig. 6. β -index and γ -index.

### 4.2. Accessibility characteristics

This section describes the evaluation of road network accessibility based on road network density (Dl and Dc ) and the average shortest distance Di between each of the two nodes. First, the road density (Dl ) and node density (Dc ) values for the main prefectural roads in the historic blocks of cities such as 1.Motomachi, 2.Makabe, and 14.Chikugoyoshii are considerably higher than those of the traditional villages. This result suggests that such road networks are dense and large in scale. By contrast, the increase rate of the values for traditional villages is more significant than that for the historic blocks in cities when the effect of narrow streets and of the analysis on the entire road network is considered. This finding reveals that the formation of the road network in traditional villages mainly relies on narrow streets that are less than 4 m wide.

 Fig. 7. Average dispersion (Di ).

### 4.3. Indirection characteristics

The detour rate (A ) for 6.Imai-choin NW1 is 2.3; this value is considerably higher than that of the other districts. Thus, the connections among the nodes in this district are weak in the road network consisting of roads that are more than 4 m wide. People on these roads must walk more than twice the linear distance on average to reach a destination point. Therefore, the indirection of the main roads in this district is strong, whereas the extent of traffic convenience is poor. The A values for 13.Iwaishima and 12.Higunto are also high because of their topographic environment. Given that island villages are generally distributed along the bay, are backed by mountains, and stand on tilted terrain, the roads in NW1 mainly assume winding forms; as a result, indirection increases in these districts. As displayed in Fig. 8 , the A values from NW1 to NW2 decrease in most island villages; thus, the narrow streets that are less than 4 m wide strengthen the linear connections among the points in the road network, improve the overall indirection, and enhance traffic efficiency within the district. By contrast, the narrow streets in the historic blocks of the cities in NW2 are primarily impassable, pouch-shaped spaces; therefore, the A value of the overall road network is higher than that of NW1.

 Fig. 8. Average detour ratio (A).

### 4.4. Clustering analysis

As detailed in the previous sections, the road network of each historic district was quantitatively analyzed in terms of circularity, accessibility, and indirection. To comprehensively understand the spatial form and structure reflected by the aforementioned characteristics, this section discusses the use of the values of the 11 indicators (e , ν , μ , μa , α , β , γ , Di , Dl , Dc , and A ) in NW1 and NW2 as variables in a clustering analysis on the 16 historic districts. The ward method was used, and the values of each indicator were standardized to unify the units of the variables. The results are shown in Fig. 9 . Four types were identified based on the differences in the road network form characteristics of various historic districts. In addition, the characteristics of each type can be clearly recognized and detailed as follows according to the radar chart of the average values of the major variables in each type (Fig. 10 ).

 Fig. 9. Similarity of road networks in the research area.

 Fig. 10. The spatial characteristics of each type.

Type 1 includes traditional villages that are located on islands and in mountain areas. These villages were naturally formed according to the primary industry. The main road networks contain few circular roads, and the road network tends to take the tree-type form; thus, the network exhibits low density, circularity, accessibility, and indirection. In the overall road network that includes narrow old streets, each indicator changes significantly; for instance, circularity and accessibility improve considerably, whereas indirection declines. Therefore, the formation of this type of road network mainly relies on roads that are less than 4 m wide. In terms of α , β , γ , the indirection of the overall road network remains poor across all the districts.

Type 2 includes settlements in the coastal areas and mainland-connected islands. These settlements were developed through ports and religious facilities. In this study, the values of each NW1 indicator are better than those of the traditional villages under Type 1; however, circularity and road network density are low among the investigated subjects. By contrast, circularity, accessibility, and indirection improve in NW2, and the values are within mid-range in general.

Type 3 includes historic districts that were developed by relying on commercial production. The main road network follows the grid pattern form, and the values of each indicator are better than those of the other types. In fact, the circularity, accessibility, and indirection of this type are ideal among all the subjects studied. Nevertheless, the values of the indicators in the overall road network (NW2) that includes narrow old streets hardly vary from those inNW1.Evendetour rate increases, thus indicating that the road networks of this type mainly consist of roads that are more than 4 m wide and stable structures. The narrow streets weakly influence the characteristics of the overall road network form.

Type 4 includes the “Jinai-cho” towns 6.Imai-cho and 7.Tondabayashi. As mentioned previously, the spatial structure of Type 4roads emphasize the traffic connections within the districts because their formation backgrounds differ from those of other districts. Therefore, the overall road network is jointly composed of roads that are more and less than 4 m wide. The analysis results reveal that, the road network forms in NW1 is incomplete because only roads that are over 4 m wide are considered. Thus, the indicators report lower values than those of other historic blocks in the same cities. Moreover, the characteristics of the road network forms are weak. In NW2 (the complete road network form), each indicator improves, and road network circularity increases significantly. In fact, this circularity is the best among all the subjects investigated in this study.

## 5. Conclusion

This study focused on the well-preserved road network forms of historic districts and analyzed the road spaces of 16 historic districts in Japan in terms of circularity, accessibility, and indirection based on graph theory. This work aimed to systematically clarify the spatial characteristics of the historic road spaces in districts with different formation backgrounds and their corresponding types. This research also endeavored to quantitatively describe the effect of road network formation on spatial characteristics. The main conclusions are presented as follows:

• In traditional villages dominated by agriculture and fishery and are dependent on natural conditions, narrow streets that are less than 4 m wide serve as auxiliary road systems to strengthen the overall connection of the road network. In a road network that functions as traffic connections to external communities and consists of roads that are more than 4 m wide, narrow streets that are less than 4 m wide further subdivide the internal grid of the districts; as a result of the highly elevated road density, the road form becomes dense and complex. Nonetheless, the narrow streets improve the circularity, accessibility, and indirection of the overall road spaces.
• In settlements of port and commercial towns formed for port trade and commercial production purposes, the main frame of the road network is composed of roads that are over 4 m wide. This network displays a complete overall form as well as ideal circularity, accessibility, and indirection. The roads that are less than 4 m wide merely serve as subsidiary spaces; they further dividing some roads in local areas and exert little effect on the spatial characteristics of the overall road network.
• Due to a historical isolated spatial mode, the districts in “Jinai-cho” towns emphasize inward traffic connection. The overall road network in such areas is jointly composed of horizontal roads that are more than 4 m wide and vertical roads that are less than 4 m wide. The removal of any of these portions renders the road network form incomplete and deteriorates road network circularity, accessibility, and indirection. The overall road network tends to take the grid form; thus, the circularity of this district type is higher than that of the remaining historic districts.

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