@article{octavio1985nonexistence, abstract = {We prove that there is no free object over a countable set in the category of complete distributive lattices with homomorphisms preserving binary meets and arbitrary joins.}, author = {Garcia, Octavio and Nelson, Evelyn}, interhash = {c4a8aeddff294dbdd727c05059ab2050}, intrahash = {d4ce23539ea3bc784068e93dc70387aa}, journal = {Order}, month = {December}, number = 4, pages = {399--403}, title = {On the nonexistence of free complete distributive lattices}, url = {http://dx.doi.org/10.1007/BF00582745}, volume = 1, year = 1985 } @article{hales1964nonexistence, author = {Hales, A. W.}, interhash = {2e2b85532b56b6caaac29b23e33f972f}, intrahash = {4d17473cee1aa8c33d821aacf2fbb95c}, journal = {Fundamentae Mathematica}, pages = {45-66}, title = {On the non-existence of free complete Boolean algebras}, url = {http://matwbn.icm.edu.pl/tresc.php?wyd=1&tom=54}, volume = 54, year = 1964 } @article{li2005towards, author = {Li, L. and Alderson, D. and Doyle, J.C. and Willinger, W.}, interhash = {5f8381f5e7d915be9eb1682ac54d1c79}, intrahash = {5d2a7bda356317c8d6a6af168128ade1}, journal = {Internet Mathematics}, number = 4, pages = {431--523}, publisher = {AK Peters}, title = {{Towards a theory of scale-free graphs: Definition, properties, and implications}}, url = {http://scholar.google.de/scholar.bib?q=info:Xi5NYPJyMvMJ:scholar.google.com/&output=citation&hl=de&as_sdt=2000&ct=citation&cd=0}, volume = 2, year = 2005 } @article{stumme98free, author = {Stumme, Gerd}, comment = {alpha}, interhash = {c5fb9e79ebca290916dac9d193033a19}, intrahash = {de157d21efb3d9723fb937be024f84cd}, journal = {{In:} {O}rder}, pages = {179-189}, title = {Free Distributive Completions of Partial Complete Lattices}, url = {http://www.kde.cs.uni-kassel.de/stumme/papers/2000/SIGKDD_Explorations00.ps}, volume = 14, year = 1998 } @article{newman03structure, author = {Newman, M. E. J.}, interhash = {7bedd01cb4c06af9f5200b0fb3faa571}, intrahash = {72bc4532c466263fde0902faee84adff}, journal = {SIAM Review}, pages = 167, title = {The structure and function of complex networks}, url = {http://www.citebase.org/abstract?id=oai:arXiv.org:cond-mat/0303516}, volume = 45, year = 2003 } @article{newman05power, author = {Newman, M. E. J.}, interhash = {7539b701d6df3fb9a90b0ff70a32bfe9}, intrahash = {436d9c707f94b26bbee4187fdf714820}, journal = {Contemporary Physics}, pages = 323, title = {Power laws, Pareto distributions and Zipf's law}, url = {doi:10.1080/00107510500052444}, volume = 46, year = 2005 } @inproceedings{boulicaut00approximation, author = {Boulicaut, Jean-Francois and Bykowski, Artur and Rigotti, Christophe}, booktitle = {Principles of Data Mining and Knowledge Discovery}, interhash = {bcaa8a570d6b987b6171c4b7aff7cacd}, intrahash = {7e53b931a9ba3d36c7536f31901376bf}, pages = {75-85}, title = {Approximation of Frequency Queris by Means of Free-Sets}, url = {citeseer.ist.psu.edu/boulicaut00approximation.html}, year = 2000 } @inproceedings{1014146, 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. }, address = {New York, NY, USA}, author = {Wu, Andrew Y. and Garland, Michael and Han, Jiawei}, booktitle = {KDD '04: Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining}, interhash = {e387dfe40f301d698bf03f338a9cda02}, intrahash = {ace73eceff27aaba6e70b390c2f3000f}, isbn = {1-58113-888-1}, pages = {719--724}, publisher = {ACM Press}, title = {Mining scale-free networks using geodesic clustering}, url = {http://doi.acm.org/10.1145/1014052.1014146}, year = 2004 } @article{ebel2002scalefree, author = {Ebel, Holger and Mielsch, Lutz-Ingo and Bornholdt, Stefan}, interhash = {87ee728e1093301d4aa2e0b98dc848af}, intrahash = {49d15163b12ae007a88578156c7cdd3f}, journal = {Physical Review E}, title = {Scale-free topology of e-mail networks}, url = {http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:cond-mat/0201476}, volume = 66, year = 2002 }