Realistic, Mathematically Tractable Graph Generation and Evolution, Using Kronecker Multiplication
Jure Leskovec, Deepay Chakrabarti, Jon Kleinberg and Christos Faloutsos
In: ECML/PKDD 2005, Porto, Portugal(2005).
How can we generate realistic graphs? In addition, how can we do so
with a mathematically tractable model that makes it feasible to
analyze their properties rigorously? Real graphs obey a long list of
surprising properties: Heavy tails for the in- and out-degree
distribution; heavy tails for the eigenvalues and eigenvectors;
small diameters; and the recently discovered ``Densification Power
Law'' (DPL). All published graph generators either fail to match
several of the above properties, are very complicated to analyze
mathematically, or both. Here we propose a graph generator that is
mathematically tractable and matches this collection of properties. The main
idea is to use a non-standard matrix operation, the Kronecker
product, to generate graphs that we refer to as ``Kronecker
We show that Kronecker graphs naturally obey all the above
properties; in fact, we can rigorously prove that they do so.
We also provide empirical evidence showing that they can mimic very
well several real graphs.
|EPrint Type:||Conference or Workshop Item (Paper)|
|Project Keyword:||Project Keyword UNSPECIFIED|
|Subjects:||Theory & Algorithms|
|Deposited By:||Jure Leskovec|
|Deposited On:||28 November 2005|