文章基本信息

标题：Properties of Stochastic Kronecker Graph
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作者：Ahmed Mehedi Nizam ; Md. Nasim Adnan ; Md. Rashedul Islam 等
期刊名称：International Journal of Computer Science Issues
印刷版ISSN：1694-0784
电子版ISSN：1694-0814
出版年度：2012
卷号：9
期号：4
出版社：IJCSI Press
摘要：The stochastic Kronecker Graph model can generate large random graph that closely resembles many real world networks. For example, the output graph has a heavy-tailed degree distribution, has a (low) diameter that effectively remains constant over time and obeys the so-called densification power law [1]. Aside from this list of very important graph properties, one may ask for some additional information about the output graph: What will be the expected number of isolated vertices? How many edges, self loops are there in the graph? What will be the expected number of triangles in a random realization? Here we try to answer the above questions. In the first phase, we bound the expected values of the aforementioned features from above. Next we establish the sufficient conditions to generate stochastic Kronecker graph with a wide range of interesting properties. Finally we show two phase transitions for the appearance of edges and self loops in stochastic Kronecker graph.
关键词：Stochastic Kronecker Graph; Isolated vertex; Edge count; Self loops; triangles; Phase transitions.