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# Dynamics of Real Networks: Patterns and Algorithms

## Abstract

With the advent of the Web, large scale social and information networks containing detailed traces of human activity have become available. This offers great opportunities to measure, model and predict actions of millions of people. For example, we had an opportunity to analyze a ``planetary scale’’ Microsoft Instant Messenger network that contains 240 million people, with more than 1 billion conversations per day (4.5TB of data), which makes it the largest social network analyzed to date. In this talk I will focus on two aspects of the dynamics of large real- world networks: (a) dynamics of information diffusion and cascading behavior in networks, and (b) dynamics of time evolving networks. First, I will consider network cascades that are created by the diffusion process where behavior spreads from node to node like an epidemic. We study two related scenarios: information diffusion among blogs, and a viral marketing setting of 16 million product recommendations among four million people. Motivated by our empirical observations we develop algorithms for finding influential bloggers and detecting disease outbreaks. We exploit the ‘‘submodularity’’ principle to develop an efficient algorithm that achieves near optimal solutions, while scaling to large problems and being 700 times faster than a simple greedy algorithm. Second, in our recent work we found interesting and counter intuitive patterns, which change some of the basic assumptions about fundamental structural properties of networks varying over time. Leveraging our observations we developed a Kronecker graph generator model that explains processes governing network evolution. Moreover, we can fit the model to large networks, and then use it to generate realistic graphs and give formal statements about their properties. Estimating the model naively takes O(N!N^2) while we develop a linear time O(E) algorithm.