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. A lot 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 a mark of normality/realism. This seminar give 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. Further, we briefly describe recent advances on some related and interesting graph problems.
Informally, a graph is set of nodes, pairs of which might be connected by edges. In a wide array of disciplines, data can be intuitively cast into this format. For example,
computer networks consist of routers/computers (nodes) and the links (edges) between them.
Social networks consist of individuals and their interconnections (which could be business
relationships or kinship or trust, etc.) Protein interaction networks link proteins which must
work together to perform some particular biological function. Ecological food webs link
species with predator-prey relationships. In these and many other fields, graphs are seemingly ubiquitous. The problems of detecting abnormalities (outliers) in a given graph and of generating synthetic but realistic graphs have received considerable attention recently. Both are tightly coupled to the problem of finding the distinguishing characteristics of real-world graphs, that is, the patterns that show up frequently in such graphs and can thus be considered as marks
of realism. A good generator will create graphs which match these patterns. Patterns and
generators are important for many applications.
Informally, a graph is set of nodes, pairs of which might be connected by edges. In a wide array of disciplines, data can be intuitively cast into this format. For example,
computer networks consist of routers/computers (nodes) and the links (edges) between them.
Social networks consist of individuals and their interconnections (which could be business
relationships or kinship or trust, etc.) Protein interaction networks link proteins which must
work together to perform some particular biological function. Ecological food webs link
species with predator-prey relationships. In these and many other fields, graphs are seemingly ubiquitous. The problems of detecting abnormalities (outliers) in a given graph and of generating synthetic but realistic graphs have received considerable attention recently. Both are tightly coupled to the problem of finding the distinguishing characteristics of real-world graphs, that is, the patterns that show up frequently in such graphs and can thus be considered as marks
of realism. A good generator will create graphs which match these patterns. Patterns and
generators are important for many applications.
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