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

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 superlinearly 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...

• Type: Conference
• Year: 2005
• Where: KDD
• Authors: Jure Leskovec, Jon M. Kleinberg, Christos Faloutsos
• Keywords: Data Mining, KDD 2005, Lucile Packard Foundation, Real Graphs, Static Graphs