Public Transport

, Volume 7, Issue 1, pp 77–99 | Cite as

A tool for measuring and visualizing connectivity of transit stop, route and transfer center in a multimodal transportation network

  • Sabyasachee MishraEmail author
  • Timothy F. Welch
  • Paul M. Torrens
  • Cheng Fu
  • Haojie Zhu
  • Eli Knaap
Original Paper


Agencies at the federal, state and local level are aiming to enhance the public transportation system (PTS) as one alternative to alleviate congestion and to cater to the needs of captive riders. To effectively act as a viable alternative transportation mode, the system must be highly efficient. One way to measure efficiency of the PTS is connectivity. In a multimodal transportation system, transit is a key component. Transit connectivity is relatively complex to calculate, as one has to consider fares, schedule, capacity, frequency and other features of the system at large. Thus, assessing transit connectivity requires a systematic approach using many diverse parameters involved in real-world service provision. In this paper, we use a graph theoretic approach to evaluate transit connectivity at various levels of service and for various components of transit, such as nodes, lines, and transfer centers in a multimodal transportation system. Further, we provide a platform for computing connectivity over large-scale applications, using visualization to communicate results in the context of their geography and to facilitate public transit decision-making. The proposed framework is then applied to a comprehensive transit network in the Washington-Baltimore region. Underpinning the visualization, we introduce a novel spatial data architecture and Web-based interface designed with free and open source libraries and crowd-sourced contextual data, accessible on various platforms such as mobile phones, tablets and personal computers. The proposed methodology is a useful tool for both riders and decision-makers in assessing transit connectivity in a multimodal transit network in a number of ways such as the identification of under-served transit areas, prioritization and allocation of funds to locations for improving transit service.


Transit connectivity Graph theory Public transportation Multimodal transportation system GIS 

List of symbols

\( D_{l}^{i} \)

Inbound distance of link l

\( D_{l}^{o} \)

Outbound distance of link l from node n to destination


Frequency of line l


Daily hours of operation of l

\( L_{{n,n_{1} }} \)

Shortest distance between node n 1 to n

\( P_{l,n}^{i} \)

Inbound connecting power of link l

\( P_{l.n}^{o} \)

Outbound connecting power of link l

\( P_{l,n}^{t} \)

Total connecting power of line l at node n


Set of stops in region R


Set of stops in line l


Set of stops in region center σ


Average speed of link l


Initial stop

\( t_{{n_{1} ,n}} \)

Transfer time from n 1 to n

\( \delta_{{n_{1} ,n_{2} }} \)

Total number of paths between n 1 and n 2

\( \delta_{{n_{1} ,n_{2} }} (n) \)

Number of paths exist between n 1 and n 2 those pass through n

\( \delta_{np} \)

A binary indicator variable for determining the degree centrality, which takes the value of 1 when node p is dependent on n, and 0 otherwise

\( \theta_{R} \)

Connectivity index for region R

\( \theta_{l} \)

Connectivity index for line l

\( \theta_{n} \)

Connectivity index for node n

\( \rho_{{n_{1} ,n}} \)

Passenger acceptance rate from node n 1 to n

\( \rho_{R} \)

Density measure for region R


Parameter for passenger acceptance rate


Parameter for passenger acceptance which is sensitive to travel time






Network system


Node dependent on n


Scaling factor coefficient for capacity of line l


Scaling factor coefficient for speed of line l


Scaling factor coefficient for distance of line l


Activity density of line l, at node n

\( \vartheta \)

Scaling factor for activity density

\( E_{l,n}^{z} \)

Number of households in zone z containing line l and node n

\( E_{l,n}^{z} \)

Employment for zone z containing line l and node n

\( \varTheta_{l,n}^{z} \)

Area of z containing line l and node

\( \varTheta_{l}^{n} \)

Number of lines l at node n

Supplementary material

12469_2014_91_MOESM1_ESM.docx (1.6 mb)
Supplementary material 1 (DOCX 1642 kb)


  1. Ahmed A, Dwyer T, Forster M et al (2006) GEOMI: GEOmetry for Maximum Insight. In: Healy P, Nikolov NS (eds) Graph drawing. Springer, Berlin, pp 468–479CrossRefGoogle Scholar
  2. Aittokallio T, Schwikowski B (2006) Graph-based methods for analysing networks in cell biology. Brief Bioinform 7:243–255. doi: 10.1093/bib/bbl022 CrossRefGoogle Scholar
  3. Barthlemy M (2004) Betweenness centrality in large complex networks. Eur Phys J B Condens Matter 38:163–168. doi: 10.1140/epjb/e2004-00111-4 Google Scholar
  4. Bell DC, Atkinson JS, Carlson JW (1999) Centrality measures for disease transmission networks. Soc Netw 21:1–21 pii: 16/S0378-8733(98)00010-0CrossRefGoogle Scholar
  5. Bonacich P (2007) Some unique properties of eigenvector centrality. Soc Netw 29:555–564 pii: 16/j.socnet.2007.04.002CrossRefGoogle Scholar
  6. Bonacich P, Lloyd P (2001) Eigenvector-like measures of centrality for asymmetric relations. Soc Netw 23:191–201 pii: 16/S0378-8733(01)00038-7CrossRefGoogle Scholar
  7. Borgatti SP (2005) Centrality and network flow. Soc Netw 27:55–71 pii: 16/j.socnet.2004.11.008CrossRefGoogle Scholar
  8. Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25:163–177. doi: 10.1080/0022250X.2001.9990249 CrossRefGoogle Scholar
  9. Carrington PJ, Scott J, Wasserman S (2005) Models and methods in social network analysis. Cambridge University Press, CambridgeGoogle Scholar
  10. Ceder A, Net YL, Coriat C (2009) Measuring public transport connectivity performance applied in Auckland, New Zealand. Transp Res Record J Transp Res Board 2111:139–147CrossRefGoogle Scholar
  11. Costenbader E, Valente TW (2003) The stability of centrality measures when networks are sampled. Soc Netw 25:283–307 pii: 16/S0378-8733(03)00012-1CrossRefGoogle Scholar
  12. Crucitti P, Latora V, Porta S (2006) Centrality in networks of urban streets. Chaos 16:015113. doi: 10.1063/1.2150162 CrossRefGoogle Scholar
  13. Derrible S, Kennedy C (2009) Network analysis of world subway systems using updated graph theory. Transp Res Record J Transp Res Board 2112:17–25. doi: 10.3141/2112-03 CrossRefGoogle Scholar
  14. Estrada E, Rodríguez-Velázquez JA (2005) Subgraph centrality in complex networks. Phys Rev E 71:056103. doi: 10.1103/PhysRevE.71.056103 CrossRefGoogle Scholar
  15. Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Netw 1:215–239 pii: 16/0378-8733(78)90021-7CrossRefGoogle Scholar
  16. Garroway CJ, Bowman J, Carr D, Wilson PJ (2008) Applications of graph theory to landscape genetics. Evol Appl 1:620–630. doi: 10.1111/j.1752-4571.2008.00047.x Google Scholar
  17. Goh K-I, Oh E, Kahng B, Kim D (2003) Betweenness centrality correlation in social networks. Phys Rev E 67:017101. doi: 10.1103/PhysRevE.67.017101 CrossRefGoogle Scholar
  18. Guimerà R, Mossa S, Turtschi A, Amaral LAN (2005) The worldwide air transportation network: anomalous centrality, community structure, and cities’ global roles. Proc Natl Acad Sci USA 102:7794–7799. doi: 10.1073/pnas.0407994102 CrossRefGoogle Scholar
  19. Hadas Y, Ceder A (2010) Public transit network connectivity. Transp Res Record J Transp Res Board 2143:1–8. doi: 10.3141/2143-01 CrossRefGoogle Scholar
  20. Hadas Y, Ceder A, Ranjitkar P (2011) Modeling public-transit connectivity with quality-of-transfer measurementsGoogle Scholar
  21. Jiang B, Claramunt C (2004) A structural approach to the model generalization of an urban street network. GeoInformatica 8:157–171. doi: 10.1023/B:GEIN.0000017746.44824.70 CrossRefGoogle Scholar
  22. Junker B, Koschutzki D, Schreiber F (2006) Exploration of biological network centralities with CentiBiN. BMC Bioinform 7:219. doi: 10.1186/1471-2105-7-219 CrossRefGoogle Scholar
  23. Lam TN, Schuler HJ (1982) Connectivity index for systemwide transit route and schedule performance. Transp Res Rec 854:17–23Google Scholar
  24. Latora V, Marchiori M (2007) A measure of centrality based on network efficiency. New J Phys 9:188. doi: 10.1088/1367-2630/9/6/188 CrossRefGoogle Scholar
  25. Liu X, Bollen J, Nelson ML, Van de Sompel H (2005) Co-authorship networks in the digital library research community. Inf Process Manage 41:1462–1480 pii: 16/j.ipm.2005.03.012CrossRefGoogle Scholar
  26. Martinez KLH, Porter BE (2006) Characterizing red light runners following implementation of a photo enforcement program. Accid Anal Prev 38:862–870. doi: 10.1016/j.aap.2006.02.011 CrossRefGoogle Scholar
  27. Mishra S, Welch TF, Jha MK (2012) Performance indicators for public transit connectivity in multi-modal transportation networks. Transp Res Part A Policy Pract 46:1066–1085. doi: 10.1016/j.tra.2012.04.006 CrossRefGoogle Scholar
  28. Moore S, Eng E, Daniel M (2003) International NGOs and the role of network centrality in humanitarian aid operations: a case study of coordination during the 2000 Mozambique floods. Disasters 27:305–318. doi: 10.1111/j.0361-3666.2003.00235.x CrossRefGoogle Scholar
  29. Newman MEJ (2004) Analysis of weighted networks. Phys Rev E 70:056131. doi: 10.1103/PhysRevE.70.056131 CrossRefGoogle Scholar
  30. Newman MEJ (2005) A measure of betweenness centrality based on random walks. Soc Netw 27:39–54 pii: 16/j.socnet.2004.11.009CrossRefGoogle Scholar
  31. Opsahl T, Agneessens F, Skvoretz J (2010) Node centrality in weighted networks: generalizing degree and shortest paths. Soc Netw 32:245–251 pii: 16/j.socnet.2010.03.006CrossRefGoogle Scholar
  32. Otte E, Rousseau R (2002) Social network analysis: a powerful strategy, also for the information sciences. J Inf Sci 28:441–453. doi: 10.1177/016555150202800601 CrossRefGoogle Scholar
  33. Özgür A, Vu T, Erkan G, Radev DR (2008) Identifying gene-disease associations using centrality on a literature mined gene-interaction network. Bioinformatics 24:i277–i285. doi: 10.1093/bioinformatics/btn182 CrossRefGoogle Scholar
  34. Park J, Kang SC (2011) A model for evaluating the connectivity of multimodal transit networks. Transportation Research Board 90th annual meetingGoogle Scholar
  35. Ruhnau B (2000) Eigenvector-centrality—a node-centrality? Soc Netw 22:357–365 pii: 16/S0378-8733(00)00031-9CrossRefGoogle Scholar
  36. White HD (2003) Pathfinder networks and author cocitation analysis: a remapping of paradigmatic information scientists. J Am Soc Inform Sci Technol 54:423–434. doi: 10.1002/asi.10228 CrossRefGoogle Scholar
  37. White DR, Borgatti SP (1994) Betweenness centrality measures for directed graphs. Soc Netw 16:335–346 pii: 16/0378-8733(94)90015-9CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sabyasachee Mishra
    • 1
    Email author
  • Timothy F. Welch
    • 2
  • Paul M. Torrens
    • 3
  • Cheng Fu
    • 3
  • Haojie Zhu
    • 4
  • Eli Knaap
    • 5
  1. 1.Department of Civil and Environmental Engineering and Intermodal Freight Transportation InstituteUniversity of MemphisMemphisUSA
  2. 2.School of City and Regional PlanningGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of Geographical Sciences and Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA
  4. 4.Department of Geographical SciencesUniversity of MarylandCollege ParkUSA
  5. 5.National Center for Smart Growth Research and Education, 054 Preinkert FieldhouseUniversity of MarylandCollege ParkUSA

Personalised recommendations