Stochastic kronecker graphs
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The document discusses stochastic Kronecker graphs (SKG), which are proposed as an efficient technique for modeling large-scale real-world networks. SKG uses Kronecker products of probability matrices to generate graphs that capture properties of natural networks, such as social networks and the web. It is hypothesized that SKG provides an efficient approach to graph mapping and generation in terms of speed and implementation for large networks. The conclusion reiterates that SKG algorithms can generate graphs with desired properties and are useful for analyzing complex systems represented as graphs.
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Stochastic kronecker graphs
- 1. Stochastic Kronecker Graphs Presenter : Zara Tariq | MSCS(A)-2015 | 1573119 | SZABIST
- 2. MOTIVATIONS(Problem Statement) The role of graph analysis is becoming increasingly important in science and industry because of the prevalence of graphs in diverse scenarios such as social networks, the Web, power grid networks, and even scientific collaboration studies. Obtaining natural graphs is hard Need better and faster algorithms in order to study them Models that accurately reflect the characteristics of real-world networks Efficiency, speed, implementation details become deciding factors Stochastic Kronecker Graphs 2/7
- 3. HYPOTHESIS Stochastic Kronecker Algorithm is an efficient graph mapping technique with respect to speed and implementation for large-scale real world networks. Stochastic Kronecker Graphs 3/7
- 4. SKG TO MODEL REAL WORLD NETWORKS Introduced by Leskovec, Chakrabarti , Kleinberg and Faloutsos Captures several well-known properties Kronecker products of probability matrices has been recently proposed as a generative model Efficient graph mapping technique for large-scale real world networks Generate any almost-natural synthetic graphs Stochastic Kronecker Graphs 4/7
- 5. CONCLUSION Graphs are a natural representation to use for the analysis of complex systems. The role of graph analysis is becoming increasingly important in science and industry because of the prevalence of graphs in diverse scenarios such as social networks, the Web, power grid networks, and even scientific collaboration studies. As we deal with large and larger graphs, the Efficiency and Speed as well as Implementation details become deciding factors in the usefulness of a model for this stochastic Kronecker Graph algorithms are capable of generating graphs with that particular properties of interest. Stochastic Kronecker Graphs 5/7
- 6. REFERENCES [1] M Mahdian, Y Xu, Stochastic kronecker graphs, Random Structures & Algorithms, 2011 [2] SI Moreno, J Neville, S Kirshner, Learning mixed kronecker product graph models with simulated method of moments, Proceedings of the 19th ACM SIGKDD, 2013. [3] S. Todorovic, Human activities as stochastic kronecker graphs, Computer VisionECCV 2012. [4] A Pinar, C Seshadhri, TG Kolda, The similarity between stochastic kronecker and chung-lu graph models, CoRR, vol. abs/1110.4925, 2011. [5] C Seshadhri, A Pinar, TG Kolda, An in-depth study of stochastic Kronecker graphs, Data Mining (ICDM), 2013. [6] Jurij Leskovec, Deepayan Chakrabarti, Jon Kleinberg, and Christos Faloutsos. Realistic, Mathematically Tractable Graph Generation and Evolution, Using Kronecker Multiplication.PKDD 2005. Stochastic Kronecker Graphs 6/7
- 7. Stochastic Kronecker Graphs 7/7
Editor's Notes
- Why are data scientists so obsessed with graphs? Its because graphs are the best tools we have for modeling the real world. • By analyzing the graph representation of a real-world structure, we can glean a variety of insights about it. Graphs that model real-world phenomena are called natural graphs, and a great deal of data science focuses on them. However, obtaining natural graphs is hard; it would be nice if we had a way to generate similar-looking graphs without the data-gathering work.• Massive graphs occur in a variety of situations, and we need to design better and faster algorithms in order to study them.• As such, there has been a great deal of research focusing on the development of models that accurately reflect the characteristics of real-world networks.• As we deal with large and larger graphs, the efficiency and speed as well as implementation details become deciding factors in the usefulness of a model. However, the benefits of having good algorithm go beyond an ability to generate large graphs, for this we have seen that Stochastic Kronecker Algorithm is an efficient graph mapping technique for large-scale real world networks.• Entering the stochastic Kronecker graph model: an easy way to generate almost-natural synthetic graphs. This paper will give an overview of natural graphs and describe the stochastic Kronecker model of generating graphs.• They also includes statistical models that are capable of modeling probability distributions over graphs and we study the basic properties of stochastic Kronecker products. Kronecker graphs were introduced by Leskovec, Chakrabarti , Kleinberg and Faloutsos [6] in order to model real world networks.• They considered a deterministic model based on Kronecker multiplication which creates graphs exhibiting several properties of real world networks like heavy tailed degree distribution and average degree that grows as a power law with the size of the graph.• They also introduced the random version of this model, called the stochastic Kronecker graph.
- Why are data scientists so obsessed with graphs? Its because graphs are the best tools we have for modeling the real world. • By analyzing the graph representation of a real-world structure, we can glean a variety of insights about it. Graphs that model real-world phenomena are called natural graphs, and a great deal of data science focuses on them. However, obtaining natural graphs is hard; it would be nice if we had a way to generate similar-looking graphs without the data-gathering work.• Massive graphs occur in a variety of situations, and we need to design better and faster algorithms in order to study them.• As such, there has been a great deal of research focusing on the development of models that accurately reflect the characteristics of real-world networks.• As we deal with large and larger graphs, the efficiency and speed as well as implementation details become deciding factors in the usefulness of a model.• The theoretical benefit of having a good, fast model is quite clear. However, the benefits of having good algorithm go beyond an ability to generate large graphs, for this we have seen that Stochastic Kronecker Algorithm is an efficient graph mapping technique for large-scale real world networks.• Entering the stochastic Kronecker graph model: an easy way to generate almost-natural synthetic graphs. This paper will give an overview of natural graphs and describe the stochastic Kronecker model of generating graphs.• They also includes statistical models that are capable of modeling probability distributions over graphs and we study the basic properties of stochastic Kronecker products. Kronecker graphs were introduced by Leskovec, Chakrabarti , Kleinberg and Faloutsos [6] in order to model real world networks.• They considered a deterministic model based on Kronecker multiplication which creates graphs exhibiting several properties of real world networks like heavy tailed degree distribution and average degree that grows as a power law with the size of the graph.• They also introduced the random version of this model, called the stochastic Kronecker graph.
- 1. Graphs are a natural representation to use for the analysis of complex systems. 2. The role of graph analysis is becoming increasingly important in science and industry because of the prevalence of graphs in diverse scenarios such as social networks, the Web, power grid networks, and even scientific collaboration studies.