Affiliation weighted networks with a differentially private degree sequence

2021 ◽  
Author(s):  
Jing Luo ◽  
Tour Liu ◽  
Qiuping Wang
Keyword(s):  
Degree Sequence ◽  
Weighted Networks

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 Scale free is not rare in international trade networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Linqing Liu ◽  
Mengyun Shen ◽  
Chang Tan
Keyword(s):  
International Trade ◽  
Preferential Attachment ◽  
Developed Countries ◽  
Total Trade ◽  
Trade Networks ◽  
Scale Free ◽  
Weighted Networks ◽  
Free Exploration ◽  
Technology Products ◽  
Attachment Mechanism

AbstractFailing to consider the strong correlations between weights and topological properties in capacity-weighted networks renders test results on the scale-free property unreliable. According to the preferential attachment mechanism, existing high-degree nodes normally attract new nodes. However, in capacity-weighted networks, the weights of existing edges increase as the network grows. We propose an optimized simplification method and apply it to international trade networks. Our study covers more than 1200 product categories annually from 1995 to 2018. We find that, on average, 38%, 38% and 69% of product networks in export, import and total trade are scale-free. Furthermore, the scale-free characteristics differ depending on the technology. Counter to expectations, the exports of high-technology products are distributed worldwide rather than concentrated in a few developed countries. Our research extends the scale-free exploration of capacity-weighted networks and demonstrates that choosing appropriate filtering methods can clarify the properties of complex networks.

scholarly journals Reconstructing the structure of directed and weighted networks of nonlinear oscillators

2017 ◽  
Vol 95 (4) ◽  
Author(s):  
Francesco Alderisio ◽  
Gianfranco Fiore ◽  
Mario di Bernardo
Keyword(s):  
Nonlinear Oscillators ◽  
Weighted Networks

scholarly journals Dynamics of hierarchical weighted networks of van der Pol oscillators

2020 ◽  
Vol 30 (12) ◽  
pp. 123146
Author(s):  
Daniel Monsivais-Velazquez ◽  
Kunal Bhattacharya ◽  
Rafael A. Barrio ◽  
Philip K. Maini ◽  
Kimmo K. Kaski
Keyword(s):  
Van Der Pol ◽  
Weighted Networks ◽  
Van Der Pol Oscillators

scholarly journals Box-covering algorithm for fractal dimension of weighted networks

2013 ◽  
Vol 3 (1) ◽  
Author(s):  
Dai-Jun Wei ◽  
Qi Liu ◽  
Hai-Xin Zhang ◽  
Yong Hu ◽  
Yong Deng ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Weighted Networks

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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