Transport network

Network science

* Theory

* Graph
* Complex network
* Contagion
* Small-world
* Scale-free
* Community structure
* Percolation
* Evolution
* Controllability
* Graph drawing
* Social capital
* Link analysis
* Optimization
* Reciprocity
* Closure
* Homophily
* Transitivity
* Preferential attachment
* Balance theory
* Network effect
* Social influence

Network types

* Informational (computing)
* Telecommunication
* Transport
* Social
* Scientific collaboration
* Biological
* Artificial neural
* Interdependent
* Semantic
* Spatial
* Dependency
* Flow
* on-Chip

Graphs
|  Features

* Clique
* Component
* Cut
* Cycle
* Data structure
* Edge
* Loop
* Neighborhood
* Path
* Vertex
* Adjacency list / matrix
* Incidence list / matrix

Types

* Bipartite
* Complete
* Directed
* Hyper
* Multi
* Random
* Weighted

* Metrics
* Algorithms

* Centrality
* Degree
* Betweenness
* Closeness
* PageRank
* Motif
* Clustering
* Degree distribution
* Assortativity
* Distance
* Modularity
* Efficiency

Models
|  Topology

* Random graph
* Erdős–Rényi
* Barabási–Albert
* Fitness model
* Watts–Strogatz
* Exponential random (ERGM)
* Random geometric (RGG)
* Hyperbolic (HGN)
* Hierarchical
* Stochastic block
* Maximum entropy
* Soft configuration
* LFR Benchmark

Dynamics

* Boolean network
* agent based
* Epidemic/SIR

* Lists
* Categories

* Topics
* Software
* Network scientists

* Category:Network theory
* Category:Graph theory

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A transport network, or transportation network is a realisation of a spatial network, describing a structure which permits either vehicular movement or flow of some commodity.[1] Examples include but are not limited to road networks, railways, air routes, pipelines, aqueducts, and power lines.

## Methods

Transport network analysis is used to determine the flow of vehicles (or people) through a transport network, typically using mathematical graph theory. It may combine different modes of transport, for example, walking and car, to model multi-modal journeys. Transport network analysis falls within the field of transport engineering. Traffic has been studied extensively using statistical physics methods.[2][3][4] Recently a real transport network of Beijing was studied using a network approach and percolation theory. The research showed that one can characterize the quality of global traffic in a city at each time in the day using percolation threshold, see Fig. 1. In recent articles, percolation theory has been applied to study traffic congestion in a city. The quality of the global traffic in a city at a given time is by a single parameter, the percolation critical threshold. The critical threshold represents the velocity below which one can travel in a large fraction of city network. The method is able to identify repetitive traffic bottlenecks. [5] Critical exponents characterizing the cluster size distribution of good traffic are similar to those of percolation theory.[6]

An empirical study regarding the size distribution of traffic jams has been performed recently by Zhang et al. [7] They found an approximate universal power law for the jam sizes distribution.

Fig. 1: Percolation of traffic networks in a typical day in Beijing. A Shows the high speed clusters. In B one can see the clusters at the critical threshold, where the giant component breaks. C Shows the low speed case where one can reach the whole city. In D, one can see the percolation behavior of the largest (green) and second largest (orange) components as a function of relative speed. E Shows the critical threshold, qc, during the day for working days and weekends. High qc means good global traffic while low qc is bad traffic--during rush hour.

## See also

* Braess' paradox
* Flow network
* Heuristic routing
* Interplanetary Transport Network
* Network science
* Percolation theory
* Street network
* Rail network
* Multimodal transport

## References

1. ↑ Barthelemy, Marc (2010). "Spatial Networks". Physics Reports 499 (1–3): 1–101. doi:10.1016/j.physrep.2010.11.002. Bibcode: 2011PhR...499....1B.
2. ↑ Helbing, D (2001). "Traffic and related self-driven many-particle systems". Reviews of Modern Physics 73 (4): 1067–1141. doi:10.1103/RevModPhys.73.1067. Bibcode: 2001RvMP...73.1067H.
3. ↑ S., Kerner, Boris (2004). The Physics of Traffic : Empirical Freeway Pattern Features, Engineering Applications, and Theory. Berlin, Heidelberg: Springer Berlin Heidelberg. ISBN 9783540409861. OCLC 840291446.
4. ↑ Wolf, D E; Schreckenberg, M; Bachem, A (June 1996) (in en-US). Traffic and Granular Flow. WORLD SCIENTIFIC. 1–394. doi:10.1142/9789814531276. ISBN 9789810226350.
5. ↑ Li, Daqing; Fu, Bowen; Wang, Yunpeng; Lu, Guangquan; Berezin, Yehiel; Stanley, H. Eugene; Havlin, Shlomo (2015-01-20). "Percolation transition in dynamical traffic network with evolving critical bottlenecks" (in en). Proceedings of the National Academy of Sciences 112 (3): 669–672. doi:10.1073/pnas.1419185112. ISSN 0027-8424. PMID 25552558. Bibcode: 2015PNAS..112..669L.
6. ↑ Switch between critical percolation modes in city traffic dynamics G Zeng, D Li, S Guo, L Gao, Z Gao, HE Stanley, S Havlin Proceedings of the National Academy of Sciences 116 (1), 23-28 (2019) Scale-free resilience of real traffic jams
7. ↑ Scale-free resilience of real traffic jams Limiao Zhang, Guanwen Zeng, Daqing Li, Hai-Jun Huang, H Eugene Stanley, Shlomo Havlin Proceedings of the National Academy of Sciences 116(18), 8673-8678 (2019)

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