document: 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 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 .
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