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SUMMARY:Recognizing graphs formed by spatial random processes - Jeanette J
 anssen (Dalhousie University)
DTSTART:20161212T160000Z
DTEND:20161212T164500Z
UID:TALK69454@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In many real life applications\, network formation can be mode
 lled using a spatial random graph model: vertices are embedded in a metric
  space S\, and pairs of vertices are more likely to be connected if they a
 re closer together in the space. A general geometric graph model that capt
 ures this concept is G(n\,w)\, where w is a&nbsp\; symmetric "link probabi
 lity" function from SxS to [0\,1]. To guarantee the spatial nature of the 
 random graph\, we requite that this&nbsp\;function has&nbsp\;the property 
 that\, for fixed x in S\, w(x\,y) decreases as y is moved further away fro
 m x. The function w can be seen as the graph limit of the sequence G(n\,w)
  as n goes to infinity.<br><span>&nbsp\;We consider the question: given a 
 large graph or sequence of graphs\, how can we determine if they are likel
 y the results of such a general geometric random graph process? Focusing o
 n the one-dimensional (linear) case where S=[0\,1]\, we define a graph par
 ameter \\Gamma and use the theory of graph limits to show that this parame
 ter indeed measures the&nbsp\;compatibility of the graph with a linear mod
 el.&nbsp\;<br>This is joint work with Huda Chuangpishit\, Mahya Ghandehari
 \, Nauzer Kalyaniwalla\, and Israel Rocha<br><br></span>
LOCATION:Seminar Room 1\, Newton Institute
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