Random graph models and their applications
(2007) Abstract
 This thesis explores different models of random graphs. The first part treats a change from the preferential attachment model
where the network incorporates new vertices and attach them
preferentially to the previous vertices with a large number of
connections. We introduce on top of this model the deletion of the
oldest connections in the system and discuss the impact on the
degree of the vertices. We show that the structure of the resulting graph doesn't
resemble the structure of the former graph.
The second and third part of the thesis concern the phase transition
in a model combining the classical random graphs model and the bond
percolation... (More)  This thesis explores different models of random graphs. The first part treats a change from the preferential attachment model
where the network incorporates new vertices and attach them
preferentially to the previous vertices with a large number of
connections. We introduce on top of this model the deletion of the
oldest connections in the system and discuss the impact on the
degree of the vertices. We show that the structure of the resulting graph doesn't
resemble the structure of the former graph.
The second and third part of the thesis concern the phase transition
in a model combining the classical random graphs model and the bond
percolation model. We describe the phase diagram on the different
parameters inherited from percolation model and classical random
graphs. We show that the phase transition is of second order similarly to the
classical random graphs and give the size of the largest connected
component above the phase transition.
In the last part, we study the spread of activation on the classical
random graph model. We give, for a given probability of connection of
the vertices, conditions on the original set of activated vertices
under which the activation diffuses through the graph and conversely,
conditions under which the activation stops before spreading to a
positive part of the graph. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/835268
 author
 Vallier, Thomas
 supervisor
 opponent

 professor Janson, Svante, Matematiska institutionen Uppsala Universitet, Uppsala.
 organization
 publishing date
 2007
 type
 Thesis
 publication status
 published
 subject
 keywords
 contact process, phase transition, classical random graphs, degree sequence, preferential attachment, percolation, random graphs
 pages
 140 pages
 publisher
 Mathematical Statistics, Centre for Mathematical Sciences, Lund University
 defense location
 Room MH:B, Matematikcentrum, SÃ¶lvegatan 18, Lund University Faculty of Engineering.
 defense date
 20080201 09:15
 ISBN
 9789162873783
 language
 English
 LU publication?
 yes
 id
 6b06008470bc4a8c82e13ecbfeb0884e (old id 835268)
 date added to LUP
 20080109 10:27:10
 date last changed
 20160919 08:45:06
@misc{6b06008470bc4a8c82e13ecbfeb0884e, abstract = {This thesis explores different models of random graphs. The first part treats a change from the preferential attachment model<br/><br> where the network incorporates new vertices and attach them<br/><br> preferentially to the previous vertices with a large number of<br/><br> connections. We introduce on top of this model the deletion of the<br/><br> oldest connections in the system and discuss the impact on the<br/><br> degree of the vertices. We show that the structure of the resulting graph doesn't<br/><br> resemble the structure of the former graph.<br/><br> <br/><br> The second and third part of the thesis concern the phase transition<br/><br> in a model combining the classical random graphs model and the bond<br/><br> percolation model. We describe the phase diagram on the different<br/><br> parameters inherited from percolation model and classical random<br/><br> graphs. We show that the phase transition is of second order similarly to the<br/><br> classical random graphs and give the size of the largest connected<br/><br> component above the phase transition.<br/><br> <br/><br> In the last part, we study the spread of activation on the classical<br/><br> random graph model. We give, for a given probability of connection of<br/><br> the vertices, conditions on the original set of activated vertices<br/><br> under which the activation diffuses through the graph and conversely,<br/><br> conditions under which the activation stops before spreading to a<br/><br> positive part of the graph.}, author = {Vallier, Thomas}, isbn = {9789162873783}, keyword = {contact process,phase transition,classical random graphs,degree sequence,preferential attachment,percolation,random graphs}, language = {eng}, pages = {140}, publisher = {ARRAY(0xa065de0)}, title = {Random graph models and their applications}, year = {2007}, }