@article{li2005towards, author = {Li, L. and Alderson, D. and Doyle, J.C. and Willinger, W.}, title = {Towards a theory of scale-free graphs: Definition, properties, and implications}, journal = {Internet Mathematics}, publisher = {AK Peters}, year = {2005}, volume = {2}, number = {4}, pages = {431--523}, url = {http://scholar.google.de/scholar.bib?q=info:Xi5NYPJyMvMJ:scholar.google.com/&output=citation&hl=de&as_sdt=2000&ct=citation&cd=0}, keywords = {free, law, network, power, scale, theory, ur} }

%0 = article %A = Li, L. and Alderson, D. and Doyle, J.C. and Willinger, W. %D = 2005 %I = AK Peters %T = Towards a theory of scale-free graphs: Definition, properties, and implications %U = http://scholar.google.de/scholar.bib?q=info:Xi5NYPJyMvMJ:scholar.google.com/&output=citation&hl=de&as_sdt=2000&ct=citation&cd=0

Many real-world graphs have been shown to be scale-free--vertex degrees follow power law distributions, vertices tend to cluster, and the average length of all shortest paths is small. We present a new model for understanding scale-free networks based on multilevel geodesic approximation, using a new data structure called a multilevel mesh.Using this multilevel framework, we propose a new kind of graph clustering for data reduction of very large graph systems such as social, biological, or electronic networks. Finally, we apply our algorithms to real-world social networks and protein interaction graphs to show that they can reveal knowledge embedded in underlying graph structures. We also demonstrate how our data structures can be used to quickly answer approximate distance and shortest path queries on scale-free networks.

@inproceedings{1014146, author = {Wu, Andrew Y. and Garland, Michael and Han, Jiawei}, title = {Mining scale-free networks using geodesic clustering}, booktitle = {KDD '04: Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining}, publisher = {ACM Press}, address = {New York, NY, USA}, year = {2004}, pages = {719--724}, url = {http://doi.acm.org/10.1145/1014052.1014146}, isbn = {1-58113-888-1}, keywords = {clustering, free, scale, mining, network}, abstract = { Many real-world graphs have been shown to be scale-free---vertex degrees follow power law distributions, vertices tend to cluster, and the average length of all shortest paths is small. We present a new model for understanding scale-free networks based on multilevel geodesic approximation, using a new data structure called a multilevel mesh.Using this multilevel framework, we propose a new kind of graph clustering for data reduction of very large graph systems such as social, biological, or electronic networks. Finally, we apply our algorithms to real-world social networks and protein interaction graphs to show that they can reveal knowledge embedded in underlying graph structures. We also demonstrate how our data structures can be used to quickly answer approximate distance and shortest path queries on scale-free networks.
} }

%0 = inproceedings %A = Wu, Andrew Y. and Garland, Michael and Han, Jiawei %B = KDD '04: Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining %C = New York, NY, USA %D = 2004 %I = ACM Press %T = Mining scale-free networks using geodesic clustering %U = http://doi.acm.org/10.1145/1014052.1014146