By Anthony Bonato, Fan Chung Graham, Pawel Pralat
This publication constitutes the lawsuits of the thirteenth overseas Workshop on Algorithms and versions for the internet Graph, WAW 2016, held in Montreal, quality controls, Canada, in December 2016.
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Extra info for Algorithms and Models for the Web Graph: 13th International Workshop, WAW 2016, Montreal, QC, Canada, December 14–15, 2016, Proceedings (Lecture Notes in Computer Science)
This random digraph model is rich enough to model power-law indegree and outdegree distributions, or power-law indegree and light-tailed outdegree distributions . Remark 4. In Theorem 1: (i) it is suﬃcient to assume that E Z1 < ∞. We note that a related result for simple (undirected) random intersection graph has been shown in . Theorem 1 extends the result of  to digraphs. 4 Diclique Clustering We investigate clustering in the random digraph D deﬁned in Sect. 2 by approximating the (random) diclique clustering coeﬃcient Cdi (D) deﬁned in (2) by a related nonrandom quantity cdi := P (I2 → I4 I1 → I3 , I1 → I4 , I2 → I3 , where (I1 , I2 , I3 , I4 ) is a random ordered quadruple of distinct nodes chosen uniformly at random.
Comb. Probab. Comput. 8(1–2), 131–159 (1999). 1017/S0963548398003459 9. : Directed random intersection graphs. In: 18th INFORMS Applied Probability Society Conference, Istanbul, Turkey, July 2015 10. : Network motifs: simple building blocks of complex networks. Science 298(5594), 824–827 (2002). org/content/298/5594/824 11. : The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003). 1137/S003614450342480 12. : Random graphs with arbitrary degree distributions and their applications.
1b. RK-approach has a higher error as well as convergence time as compared to SA-approach. (a) Comparison of Kaczmarz implementation of all the three methods. In dotted is shown the theoretical classiﬁcation error (TCE). (b) Comparison of Kaczmarz, power iteration and stochastic approximation implementation of normalized Laplacian. Fig. 3. Performance on Gaussian mixture model graph of 10000 nodes. 4 Online Learning In the RK-approach as well as SA-approach, the classiﬁcation function is updated only for one or few nodes in one step.