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Properties of Stochastic Kronecker Graph | Ahmed Mehedi Nizam
; Md. Nasim Adnan
; Md. Rashedul Islam
; Mohammad Akbar Kabir
; | Date: |
4 Oct 2012 | Abstract: | 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. | Source: | arXiv, 1210.1300 | Services: | Forum | Review | PDF | Favorites |
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