scholarly journals Win-Win Kernelization for Degree Sequence Completion Problems

2014 ◽  
pp. 194-205 ◽  
Author(s):  
Vincent Froese ◽  
André Nichterlein ◽  
Rolf Niedermeier
Keyword(s):  
Degree Sequence ◽  
Completion Problems

scholarly journals A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs

Algorithmica ◽  
2018 ◽  
Vol 81 (4) ◽  
pp. 1584-1614 ◽  
Author(s):  
Robert Bredereck ◽  
Vincent Froese ◽  
Marcel Koseler ◽  
Marcelo Garlet Millani ◽  
André Nichterlein ◽  
...  
Keyword(s):  
Directed Graphs ◽  
Degree Sequence ◽  
Parameterized Algorithmics ◽  
Completion Problems

scholarly journals Win-win kernelization for degree sequence completion problems

2016 ◽  
Vol 82 (6) ◽  
pp. 1100-1111 ◽  
Author(s):  
Vincent Froese ◽  
André Nichterlein ◽  
Rolf Niedermeier
Keyword(s):  
Degree Sequence ◽  
Completion Problems

The configuration model

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Degree Sequence ◽  
Graph Model ◽  
Network Models ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Configuration Model ◽  
Bipartite Networks ◽  
Small Component ◽  
Random Graph Model ◽  
Average Size

A discussion of the most fundamental of network models, the configuration model, which is a random graph model of a network with a specified degree sequence. Following a definition of the model a number of basic properties are derived, including the probability of an edge, the expected number of multiedges, the excess degree distribution, the friendship paradox, and the clustering coefficient. This is followed by derivations of some more advanced properties including the condition for the existence of a giant component, the size of the giant component, the average size of a small component, and the expected diameter. Generating function methods for network models are also introduced and used to perform some more advanced calculations, such as the calculation of the distribution of the number of second neighbors of a node and the complete distribution of sizes of small components. The chapter ends with a brief discussion of extensions of the configuration model to directed networks, bipartite networks, networks with degree correlations, networks with high clustering, and networks with community structure, among other possibilities.

scholarly journals Data completion problems solved as Nash games

2012 ◽  
Vol 386 ◽  
pp. 012004 ◽  
Author(s):  
A Habbal ◽  
M Kallel
Keyword(s):  
Nash Games ◽  
Data Completion ◽  
Completion Problems

scholarly journals How likely is an i.i.d. degree sequence to be graphical?

2005 ◽  
Vol 15 (1B) ◽  
pp. 652-670 ◽  
Author(s):  
Richard Arratia ◽  
Thomas M. Liggett
Keyword(s):  
Degree Sequence

scholarly journals Random graphs with a given degree sequence

2011 ◽  
Vol 21 (4) ◽  
pp. 1400-1435 ◽  
Author(s):  
Sourav Chatterjee ◽  
Persi Diaconis ◽  
Allan Sly
Keyword(s):  
Random Graphs ◽  
Degree Sequence
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