Graph Mining: Laws and Generators

Abstract

How does the Web look? How could we tell an “abnormal” social network from a “normal” one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks, to sociology, to biology, and many more. Indeed, any M : N relation in database terminology can be represented as a graph. Many of these questions boil down to the following: “How can we generate synthetic but realistic graphs?” To answer this, we must first understand what patterns are common in real-world graphs, and can thus be considered amark of normality/realism. This survey gives an overview of the incredible variety of work that has been done on these problems. One of our main contributions is the integration of points of view from physics, mathematics, sociology and computer science.