GoMore Network AnalysisKate LyndegaardGEOG 596AMentor: Frank Hardisty

Outline

1. Motivation and summary2. What is network analysis?3. The project objective4. The GoMore network5. The preliminary results6. The next steps7. Thanks

Motivation and Summary

Motivation and Summary- How can we begin to discuss integration of spatial analysis and

social network analysis intersect?

- Are there elements of geospatial/geostatistical theory which complement social network theoretic approaches to examining context and relationships in networks, and vice versa?

Motivation and Summary- How can we begin to discuss integration of spatial analysis and

social network analysis intersect?

- Are there elements of geospatial/geostatistical theory which complement social network theoretic approaches to examining context and relationships in networks, and vice versa?

What is network analysis?

Network RepresentationA network represents data as a series of ‘nodes’ and ‘edges’

Node

Edge

Directed NetworksA directed network represents the directionality of events represented by ‘edges’

Weighted NetworksNot all networks are represented by edges sharing equal values.

Weighted networks attribute additional data to every edge.

15

15

10

2

2

2

2

6

Topological Properties: DegreeCentrality measures such as ‘degree’ measure the relative importance of a node within a network.

Degree = 5

Out degree = 3

In degree = 2Out degree = 1

Source: Lotan, G.: Network X and Gephi, NYC PyData Conference 2012

Topological Properties: Path Length

Path length measures the number of edges between two nodes.

Shortest path length, and average path length (calculated over the entire graph), may also be measured.

12

45

3

6

Path Length = 2

The Project Objective.

Analyze the GoMore Network• Analyze the network of Northern Europe’s leading, online ride-share

provider: GoMore (www.GoMore.dk)

Analyze the GoMore Network1. Examine a number of topological network properties in

order to characterize the interconnectivity of GoMore travel

2. Examine weighted network properties in order to analyze the significance of the volume of travel

3. Determine whether or not there is a correlation between population density and the volume of travel between network nodes

The GoMore network.

Creating the Network Graph

Technologies employed:• PostgreSQL: Advanced SQL queries to structure data• Gephi: Generate .GML (graph file), visualization,

analyses• igraph as R package: Implement network analysis

algorithms• R: Implement statistical methods, visualization• ArcGIS for Desktop: Spatial analyses, visualization,

feature attribution, processing of demographic data

Creating the Network Graph: PostgreSQL

‘nodes’ table

Creating the Network Graph: PostgreSQL

‘edges’ table

Creating the Network Graph: Gephi

GoMore network graph: Circular Layout

Creating the Network Graph: ArcGIS

Creating the Network Graph: ArcGIS

The Preliminary Results.

Topological Properties of the GoMore Network

Comparative Model: Erdős-Rényi random graph

Power Law Degree Distribution

Clustering Spectrum: Average Local Clustering Coefficient vs. degree

Source: Barabási, A.L.: Network Science. Forthcoming, pp. 41

Average Nearest Neighbor vs. Degree

The Next Steps.

The GoMore Network and Population Data

Next Steps1. Complete and refine weighted network analyses

2. Refine spatial analyses

3. Discuss correlations between network and spatial analyses

4. Complete journal article for peer-review (GIScience 2014, Vienna, Austria)

ReferencesAlbert, R., Barabási, A. L.: Topology of evolving networks: local events and universality. Physical review letters 85.24, 5234 (2000).Barabási, A.L.: Network Science. Forthcoming.Barabási, A.L., Albert, R.: Emergence of Scaling in Random Networks. Science 286.5439, 509-512 (1999) Barthélemy, M., Barrat, A., Pastor-Satorras, R., Vespignani, A.: Characterization and modeling of weighted networks. Physica a: Statistical mechanics and its applications 346.1, 34-43 (2005)Barrat, A., Barthelemy, M., Pastor-Satorras, R., Vespignani, A.: The architecture of complex weighted networks. PNAS 101.11, 3747-3752 (2004)Clauset, A., Shalizi, C. R., Newman, M. E.: Power-law distributions in empirical data. SIAM Review 51.4, 661-703 (2009)De Montis, A., Barthélemy, M., Chessa, A., Vespignani, A.: The structure of inter-urban traffic: A weighted network analysis. arXiv preprint physics/0507106 (2005)De Montis, A., Caschili, S., Chessa, A.: Spatial Complex Network Analysis and Accessibility Indicators: the Case of Municipal Commuting in Sardinia, Italy. EJTIR 4.11, (2011)De Montis, A., Chessa, A., Campagna, M., Caschili, S., Deplano, G.: Modeling commuting systems through a complex network analysis: A study of the Italian islands of Sardinia and Sicily. Journal of Transport and Land Use 2.3, (2010)Easley, D., Kleinberg, J.: Networks, crowds, and markets. Cambridge, Cambridge University Press (2010)Erdős, P., Rényi, A.: On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutató Int. Közl 5, 17-61 (1960).Gallego, F. J.: A population density grid of the European Union. Population and Environment 31.6, 460-473 (2010).Gastner, M. T., Newman, M. E.: The spatial structure of networks. Eur. Phys. J. B 49.2, 247-252 (2006)Gorman, S. P., Kulkarni, R.: Spatial small worlds: new geographic patterns for an information economy. arXiv preprint cond-mat/0310426, (2003)Liben-Nowell, D., Novak, J., Kumar, R., Raghavan, P., Tomkins, A.: Geographic routing in social networks. PNAS 102.33, 11623-11628 (2005)Newman, M. E.: Analysis of weighted networks. Physical Review E 70.5, 056131(2004).Onnela, J. P., Saramäki, J., Kertész, J., Kaski, K.: Intensity and coherence of motifs in weighted complex networks. Physical Review E 71.6, 065103 (2005)Patuelli, R., Reggiani, A., Gorman, S. P., Nijkamp, P., Bade, F. J.: Network analysis of commuting flows: A comparative static approach to German data. Networks and Spatial Economics 7.4, 315-331 (2007)Travers, J., Milgram, S.: An experimental study of the small world problem. Sociometry 4, 425-443 (1969)Watts, D. J., Strogatz, S. H.: Collective dynamics of ‘small-world’networks. Nature 393.6684, 440-442 (1998)Yook, S. H., Jeong, H., Barabási, A. L.: Modeling the Internet's large-scale topology. PNAS 99.21, 13382-13386 (2002).

ThanksI would like to thank Beth King and Frank Hardisty