TY - JOUR AU - Li, L. AU - Alderson, D. AU - Doyle, J.C. AU - Willinger, W. T1 - Towards a theory of scale-free graphs: Definition, properties, and implications JO - Internet Mathematics PY - 2005/ VL - 2 IS - 4 SP - 431 EP - 523 UR - http://scholar.google.de/scholar.bib?q=info:Xi5NYPJyMvMJ:scholar.google.com/&output=citation&hl=de&as_sdt=2000&ct=citation&cd=0 M3 - KW - free KW - law KW - network KW - power KW - scale KW - theory KW - ur L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Newman, M. E. J. T1 - Power laws, Pareto distributions and Zipf's law JO - Contemporary Physics PY - 2005/ VL - 46 IS - SP - EP - UR - doi:10.1080/00107510500052444 M3 - KW - distribution KW - free KW - law KW - long KW - power KW - scale KW - tail KW - zipf L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Wu, Andrew Y. AU - Garland, Michael AU - Han, Jiawei A2 - T1 - Mining scale-free networks using geodesic clustering T2 - KDD '04: Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining PB - ACM Press CY - New York, NY, USA PY - 2004/ M2 - VL - IS - SP - 719 EP - 724 UR - http://doi.acm.org/10.1145/1014052.1014146 M3 - KW - clustering KW - free KW - scale KW - mining KW - network L1 - SN - 1-58113-888-1 N1 - N1 - AB - 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.

ER - TY - JOUR AU - Newman, M. E. J. T1 - The structure and function of complex networks JO - SIAM Review PY - 2003/ VL - 45 IS - SP - EP - UR - http://www.citebase.org/abstract?id=oai:arXiv.org:cond-mat/0303516 M3 - KW - complex KW - free KW - law KW - long KW - networks KW - power KW - scale KW - tail L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Ebel, Holger AU - Mielsch, Lutz-Ingo AU - Bornholdt, Stefan T1 - Scale-free topology of e-mail networks JO - Physical Review E PY - 2002/ VL - 66 IS - SP - EP - UR - http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:cond-mat/0201476 M3 - KW - free KW - scale KW - email KW - seminar2006 KW - networks L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Boulicaut, Jean-Francois AU - Bykowski, Artur AU - Rigotti, Christophe A2 - T1 - Approximation of Frequency Queris by Means of Free-Sets T2 - Principles of Data Mining and Knowledge Discovery PB - CY - PY - 2000/ M2 - VL - IS - SP - 75 EP - 85 UR - citeseer.ist.psu.edu/boulicaut00approximation.html M3 - KW - Analysis KW - Concept KW - Formal KW - closed KW - dm KW - fca KW - free KW - itemset KW - itemsets KW - kdd KW - mining KW - sets L1 - SN - N1 - Approximation of Frequency Queries By Means of Free-Sets - Boulicaut, Bykowski, Rigotti (ResearchIndex) N1 - AB - ER - TY - JOUR AU - Stumme, Gerd T1 - Free Distributive Completions of Partial Complete Lattices JO - In: Order PY - 1998/ VL - 14 IS - SP - 179 EP - 189 UR - http://www.kde.cs.uni-kassel.de/stumme/papers/2000/SIGKDD_Explorations00.ps M3 - KW - 1998 KW - analysis KW - complete KW - completions KW - concept KW - distributive KW - distributivity KW - fca KW - formal KW - free KW - lattice KW - lattices KW - myown KW - theory L1 - SN - N1 - Publications of Gerd Stumme N1 - AB - ER - TY - JOUR AU - Garcia, Octavio AU - Nelson, Evelyn T1 - On the nonexistence of free complete distributive lattices JO - Order PY - 1985/12 VL - 1 IS - 4 SP - 399 EP - 403 UR - http://dx.doi.org/10.1007/BF00582745 M3 - KW - distributive KW - fca KW - free KW - lattice KW - nonexistence KW - variety L1 - SN - N1 - SpringerLink - Abstract N1 - AB - 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. ER - TY - JOUR AU - Hales, A. W. T1 - On the non-existence of free complete Boolean algebras JO - Fundamentae Mathematica PY - 1964/ VL - 54 IS - SP - 45 EP - 66 UR - http://matwbn.icm.edu.pl/tresc.php?wyd=1&tom=54 M3 - KW - algebras KW - boolean KW - complete KW - existence KW - fca KW - free KW - lattice L1 - SN - N1 - Proof, that no there are no free complete lattices N1 - AB - ER -