# A Geometric Classification of World Urban Road Networks

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## Abstract

**:**

## 1. Introduction

## 2. Network Science

## 3. Materials and Methods

#### 3.1. Data

#### 3.2. Methodology

#### 3.2.1. Degree Distribution

#### 3.2.2. Link Length Distribution

#### 3.2.3. Intersection Angle Distribution

_{1}to j

_{4}, then it creates four angles that sum to 360°. For a given node $i$ and its connected nodes $j$, each angle is calculated for node $i$ and two nodes, e.g., ${j}_{1}$ and ${j}_{2}$, that are adjacent to each other. As an example, consider the triangle $\angle {j}_{1}i{j}_{2}$ to calculate the angle A shown in Figure 1. Since the information of latitudes and longitudes of the nodes $i$, ${j}_{1}$, and ${j}_{2}$, and link lengths of $i\to {j}_{1}$ and $i\to {j}_{2}$ are known, we can calculate the distance between ${j}_{1}\to {j}_{2}$ using the Haversine formula [64]. The angle is then calculated using the Cosine rule:

#### 3.2.4. Clustering

## 4. Results

#### 4.1. Universal Pattern

^{2}value of 0.99 for this fit. This result suggests the presence of a universal mechanism that directs the road network growth. In other words, this relationship shows that on average each node is connected to 1.33 links, and this trend is found to be universally true for all cities regardless of when the road network was developed.

#### 4.2. Road Network Analysis

## 5. Discussion

#### 5.1. Cities Classification

#### 5.2. Research and Policy Implications

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Calculating angle of A made by links $i{j}_{1}$ and $i{j}_{2}$ at node $i$ using the Cosine rule.

Percentiles | Length (m) |
---|---|

10 | 15 |

20 | 27 |

30 | 41 |

40 | 55 |

50 | 73 |

60 | 93 |

70 | 121 |

80 | 170 |

90 | 279 |

Clustering Techniques | Silhouette Scores |
---|---|

K-means | 0.69 |

Spectral K-means | 0.66 |

Hierarchical | 0.63 |

HDBSCAN | 0.47 |

Group | Cities |
---|---|

Class 1: Gridiron (many 90° angles) | Baghdad, Buenos Aires, Delhi, Karachi, Lahore, Lima, Santiago. |

Class 2: Long Link (disproportionate number of long links) | Beijing, Chengdu, Chongqing, Dalian, Dongguan, Fuzhou, Guangzhou, Hangzhou, Harbin, Nanjing, Qingdao, Quanzhou, Shanghai, Shenyang, Suzhou, Tianjin, Wuhan, Xianyang, Zhengzhou. |

Class 3: Organic (short links and more non-90° and 180° angles) | Barcelona, Istanbul, London, Madrid, Milan, Moscow, Naples, Paris, Rome, Saint Petersburg. |

Class 4: Hybrid (historical and recently developed with both short and long links) | Abidjan, Bangdung, Bangkok, Belo Horizonte, Bengaluru, Bogota, Calcutta, Chennai, Chicago, Dhaka, Ho Chi Minh, Hyderabad, Jakarta, Los Angeles, Manila, Medellin, Miami, Phoenix, Porto Alegre, Recife, Surabaya, Tehran, Tokyo. |

Class 5: Mixed (shares similarity with all other classes) | Ahmedabad, Ankara, Atlanta, Boston, Dallas, Detroit, Houston, Johannesburg, Mumbai, New York, Philadelphia, Pune, Rio de Janeiro, Salvador, San Francisco, Sao Paolo, Seoul, Shenzhen, Surat, Taipei, Washington DC. |

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**MDPI and ACS Style**

Badhrudeen, M.; Derrible, S.; Verma, T.; Kermanshah, A.; Furno, A.
A Geometric Classification of World Urban Road Networks. *Urban Sci.* **2022**, *6*, 11.
https://doi.org/10.3390/urbansci6010011

**AMA Style**

Badhrudeen M, Derrible S, Verma T, Kermanshah A, Furno A.
A Geometric Classification of World Urban Road Networks. *Urban Science*. 2022; 6(1):11.
https://doi.org/10.3390/urbansci6010011

**Chicago/Turabian Style**

Badhrudeen, Mohamed, Sybil Derrible, Trivik Verma, Amirhassan Kermanshah, and Angelo Furno.
2022. "A Geometric Classification of World Urban Road Networks" *Urban Science* 6, no. 1: 11.
https://doi.org/10.3390/urbansci6010011