APS Poster10people.maths.ox.ac.uk/~porterm/papers/APSPosterFinal3.pdf · 2009. 3. 26. · Title:...
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Visualization of Communities in Networks Amanda Traud, University of North Carolina at Chapel Hill, Christina Frost, College of Saint Scholastica, Peter J. Mucha, University of North Carolina at Chapel Hill, Mason A. Porter, University of Oxford Mason A. Porter, University of Oxford Caltech Facebook Network Dominant Characteristic: House Nodes: 762 The Facebook networks are defined from self-identified, reciprocal "friendships." Nodes: 762 Edges: 16651 Communities: 11 Unknown Lloyd Caltech Houses Avery Blacker Dabney Fleming Page Ricketts Ruddock 1-Albert, R 2-Barabasi, A Reed Facebook Network 2-Barabasi, A 3-Jeong, H 4-Oltvai, Z 5-Newman, M 6-Pastor-Satorras, R 7-Vespignani, A Reed Facebook Network Dominant Characteristic : Year Nodes: 962 Edges: 18812 Communities: 6 7-Vespignani, A 8-Watts, D 9-Moreno, Y 10-Vazquez, A Communities: 6 Reed Years Freshmen Sophomores Juniors Seniors Visualizing the social networks in this poster was a multiple-step process. For each network, we identified communities of the largest connected component using a modified version of the algorithm in [3]. Namely, we heuristically maximized the quality function known as modularity, which measures the weight of within-community edges versus between-community edges for a Haverford Facebook Network Dominant Characteristic : Year Nodes: 1446 Edges: 59589 Network Scientists Seniors which measures the weight of within-community edges versus between-community edges for a partition of a graph, using a spectral method followed by Kernighan-Lin node-swapping steps between communities. To determine the community placement (the coordinates of their centers) in our visualizations, we use the Fruchterman-Reingold algorithm [1], a force-directed layout method that is closely related to modularity maximization [4], treating the communities themselves as the nodes of a (significantly smaller) network with connections weighted by rescaled inter-community links. We then use the Kamada-Kawaii spring-embedding graph visualization algorithm [2] to place the nodes of each individual community (ignoring inter- community links) and then to rotate and flip the communities for optimal placement (including inter-community links). Our pie chart visualizations show the attributes of communities rather than individual nodes using the same Fruchterman-Reingold coordinates. The network of network scientists, compiled by Mark Newman [3], has nodes given by people and edges based on paper co-authorship. We label the 10 nodes with the largest-magnitude two-dimensional vertex vectors from the initial Edges: 59589 Communities: 5 Network Scientists Color Scheme: Community Nodes: 379 Edges: 914 Communities: 36 Freshmen Haverford Years References [1] T. M. J. Fruchtermanand E. M. Reingold, Graph drawing by force-directed placement, Software --Practice and Experience, Vol. 21, pp. 1129-1164 (1991). [2] T. Kamadaand S. Kawai, An algorithm for drawing general undirected graphs, Information Processing Letters, Vol. 31, pp. 7-15 (1989). [3] M. E. J. Newman, Finding community structure in networks using eigenvectors of matrices, Physical Review E, Vol. 74, No. 036104 (2006). [4] A. Noack, Modularity clustering is force-directed layout, arXiv:0807.4052 (2008). [5] M. A. Porter, J.-P. Onnela, and P. J. Mucha, Communities in Networks, arXiv:0902.3788 (2009). [6] A. L. Traud, E. D. Kelsic, P. J. Mucha, and M. A. Porter, Community Structure in Online Collegiate Social networks, arXiv:0809.0960 (2008). than individual nodes using the same Fruchterman-Reingold coordinates. Acknowledgements We thank Mark Newman and Adam D'Angelo/Facebook for data, Eric Kelsic for his preliminary work on this project, and Aaron Clauset for his valuable insight. This research was supported in part by the National Science Foundation HRD-0450099, DMS-0645369. two-dimensional vertex vectors from the initial step of the spectral community-detection algorithm we employed. Freshmen Sophomores Juniors Seniors http://netwiki.amath.unc.edu
Transcript of APS Poster10people.maths.ox.ac.uk/~porterm/papers/APSPosterFinal3.pdf · 2009. 3. 26. · Title:...
Visualization of Communities in NetworksAmanda Traud, University of North Carolina at Chapel Hill,
Christina Frost, College of Saint Scholastica,
Peter J. Mucha, University of North Carolina at Chapel Hill,
Mason A. Porter, University of OxfordMason A. Porter, University of Oxford
Caltech Facebook Network
Dominant Characteristic: House
Nodes: 762
The Facebook networks are
defined from self-identified, reciprocal "friendships."
Nodes: 762
Edges: 16651
Communities: 11
Unknown LloydCaltech Houses
Unknown
Avery
Blacker
Dabney
Fleming
Lloyd
Page
Ricketts
Ruddock
1-Albert, R
2-Barabasi, AReed Facebook Network
2-Barabasi, A
3-Jeong, H
4-Oltvai, Z
5-Newman, M
6-Pastor-Satorras, R
7-Vespignani, A
Reed Facebook Network
Dominant Characteristic : Year
Nodes: 962
Edges: 18812
Communities: 6 7-Vespignani, A
8-Watts, D
9-Moreno, Y
10-Vazquez, A
Communities: 6
Reed Years
Freshmen
Sophomores
Juniors
Seniors
Visualizing the social networks in this poster was a multiple-step process. For each network, we
identified communities of the largest connected component using a modified version of the
algorithm in [3]. Namely, we heuristically maximized the quality function known as modularity,
which measures the weight of within-community edges versus between-community edges for a
Haverford Facebook Network
Dominant Characteristic : Year
Nodes: 1446
Edges: 59589 Network Scientists
Seniors
which measures the weight of within-community edges versus between-community edges for a
partition of a graph, using a spectral method followed by Kernighan-Lin node-swapping steps
between communities. To determine the community placement (the coordinates of their centers)
in our visualizations, we use the Fruchterman-Reingold algorithm [1], a force-directed layout
method that is closely related to modularity maximization [4], treating the communities
themselves as the nodes of a (significantly smaller) network with connections weighted by
rescaled inter-community links. We then use the Kamada-Kawaii spring-embedding graph
visualization algorithm [2] to place the nodes of each individual community (ignoring inter-
community links) and then to rotate and flip the communities for optimal placement (including
inter-community links). Our pie chart visualizations show the attributes of communities rather
than individual nodes using the same Fruchterman-Reingold coordinates.
The network of network scientists, compiled by
Mark Newman [3], has nodes given by people
and edges based on paper co-authorship. We
label the 10 nodes with the largest-magnitude
two-dimensional vertex vectors from the initial
Edges: 59589
Communities: 5Network Scientists
Color Scheme: Community
Nodes: 379
Edges: 914
Communities: 36Freshmen
Haverford Years
References[1] T. M. J. Fruchterman and E. M. Reingold, Graph drawing by force-directed placement, Software -- Practice and Experience, Vol. 21, pp. 1129-1164 (1991).
[2] T. Kamada and S. Kawai, An algorithm for drawing general undirected graphs, Information Processing Letters, Vol. 31, pp. 7-15 (1989).
[3] M. E. J. Newman, Finding community structure in networks using eigenvectors of matrices, Physical Review E, Vol. 74, No. 036104 (2006).
[4] A. Noack, Modularity clustering is force-directed layout, arXiv:0807.4052 (2008).
[5] M. A. Porter, J.-P. Onnela, and P. J. Mucha, Communities in Networks, arXiv:0902.3788 (2009).
[6] A. L. Traud, E. D. Kelsic, P. J. Mucha, and M. A. Porter, Community Structure in Online Collegiate Social networks, arXiv:0809.0960 (2008).
than individual nodes using the same Fruchterman-Reingold coordinates.
AcknowledgementsWe thank Mark Newman and Adam D'Angelo/Facebook for data, Eric Kelsic for his preliminary work on this project, and Aaron Clauset for
his valuable insight. This research was supported in part by the National Science Foundation HRD-0450099, DMS-0645369.
two-dimensional vertex vectors from the initial
step of the spectral community-detection
algorithm we employed.
Freshmen
Sophomores
Juniors
Seniors
http://netwiki.amath.unc.edu
