Graphs over time: densification laws, shrinking diameters and possible explanations Export

@inproceedings{citeulike:505952, abstract = {How do real graphs evolve over time? What are "normal" growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs , identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time.Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing super-linearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) or O(log(log n)).Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a "forest fire" spreading process, that has a simple, intuitive justification, requires very few parameters (like the "flammability" of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study.}, address = {New York, NY, USA}, author = {Leskovec, Jure and Kleinberg, Jon and Faloutsos, Christos}, booktitle = {KDD '05: Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining}, citeulike-article-id = {505952}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=1081870.1081893}, citeulike-linkout-1 = {http://dx.doi.org/10.1145/1081870.1081893}, doi = {10.1145/1081870.1081893}, isbn = {1-59593-135-X}, keywords = {community\_evolution, data\_mining, graphs}, location = {Chicago, Illinois, USA}, pages = {177--187}, posted-at = {2008-06-13 13:10:41}, priority = {0}, publisher = {ACM}, title = {Graphs over time: densification laws, shrinking diameters and possible explanations}, url = {http://dx.doi.org/10.1145/1081870.1081893}, year = {2005} }

TY - CONF ID - citeulike:505952 L3 - citeulike-article-id:505952 N2 - How do real graphs evolve over time? What are "normal" growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs , identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time.Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing super-linearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) or O(log(log n)).Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a "forest fire" spreading process, that has a simple, intuitive justification, requires very few parameters (like the "flammability" of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. CY - Chicago, Illinois, USA SN - 1-59593-135-X AD - New York, NY, USA EP - 187 TI - Graphs over time: densification laws, shrinking diameters and possible explanations PB - ACM T2 - KDD '05: Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining SP - 177 KW - community_evolution KW - data_mining KW - graphs AU - Leskovec, Jure AU - Kleinberg, Jon AU - Faloutsos, Christos PY - 2005/// UR - http://dx.doi.org/10.1145/1081870.1081893 ER -