June  2008, 3(2): 277-294. doi: 10.3934/nhm.2008.3.277

Augmenting $k$-core generation with preferential attachment

1. 

Faculty of Informatics, Universität Karlsruhe (TH), 78131 Karlsruhe, Germany, Germany, Germany, Germany, Germany

Received  August 2007 Revised  March 2008 Published  March 2008

The modeling of realistic networks is of prime importance for modern complex systems research. Previous procedures typically model the natural growth of networks by means of iteratively adding nodes, geometric positioning information, a definition of link connectivity based on the preference for nearest neighbors or already highly connected nodes, or combine several of these approaches.
Our novel model brings together the well-know concepts of $k$-cores, originally introduced in social network analysis, and of preferential attachment. Recent studies exposed the significant $k$-core structure of several real world systems, e.g., the AS network of the Internet. We present a simple and efficient method for generating networks which at the same time strictly adhere to the characteristics of a given $k$-core structure, called core fingerprint, and feature a power-law degree distribution. We showcase our algorithm in a com- parative evaluation with two well-known AS network generators.
Citation: Michael Baur, Marco Gaertler, Robert Görke, Marcus Krug, Dorothea Wagner. Augmenting $k$-core generation with preferential attachment. Networks & Heterogeneous Media, 2008, 3 (2) : 277-294. doi: 10.3934/nhm.2008.3.277
[1]

Manuel Friedrich, Martin Kružík, Jan Valdman. Numerical approximation of von Kármán viscoelastic plates. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 299-319. doi: 10.3934/dcdss.2020322

[2]

Yunping Jiang. Global graph of metric entropy on expanding Blaschke products. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1469-1482. doi: 10.3934/dcds.2020325

[3]

Gökhan Mutlu. On the quotient quantum graph with respect to the regular representation. Communications on Pure & Applied Analysis, 2021, 20 (2) : 885-902. doi: 10.3934/cpaa.2020295

[4]

Huijuan Song, Bei Hu, Zejia Wang. Stationary solutions of a free boundary problem modeling the growth of vascular tumors with a necrotic core. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 667-691. doi: 10.3934/dcdsb.2020084

[5]

Vaibhav Mehandiratta, Mani Mehra, Günter Leugering. Fractional optimal control problems on a star graph: Optimality system and numerical solution. Mathematical Control & Related Fields, 2021, 11 (1) : 189-209. doi: 10.3934/mcrf.2020033

[6]

Xiyou Cheng, Zhitao Zhang. Structure of positive solutions to a class of Schrödinger systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020461

[7]

Toshiko Ogiwara, Danielle Hilhorst, Hiroshi Matano. Convergence and structure theorems for order-preserving dynamical systems with mass conservation. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3883-3907. doi: 10.3934/dcds.2020129

[8]

Adrian Viorel, Cristian D. Alecsa, Titus O. Pinţa. Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020407

[9]

Pablo Neme, Jorge Oviedo. A note on the lattice structure for matching markets via linear programming. Journal of Dynamics & Games, 2020  doi: 10.3934/jdg.2021001

[10]

Vaibhav Mehandiratta, Mani Mehra, Günter Leugering. Existence results and stability analysis for a nonlinear fractional boundary value problem on a circular ring with an attached edge : A study of fractional calculus on metric graph. Networks & Heterogeneous Media, 2021  doi: 10.3934/nhm.2021003

[11]

Xin-Guang Yang, Lu Li, Xingjie Yan, Ling Ding. The structure and stability of pullback attractors for 3D Brinkman-Forchheimer equation with delay. Electronic Research Archive, 2020, 28 (4) : 1395-1418. doi: 10.3934/era.2020074

[12]

Feimin Zhong, Jinxing Xie, Yuwei Shen. Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020172

[13]

Pavel Eichler, Radek Fučík, Robert Straka. Computational study of immersed boundary - lattice Boltzmann method for fluid-structure interaction. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 819-833. doi: 10.3934/dcdss.2020349

[14]

Vadim Azhmyakov, Juan P. Fernández-Gutiérrez, Erik I. Verriest, Stefan W. Pickl. A separation based optimization approach to Dynamic Maximal Covering Location Problems with switched structure. Journal of Industrial & Management Optimization, 2021, 17 (2) : 669-686. doi: 10.3934/jimo.2019128

2019 Impact Factor: 1.053

Metrics

  • PDF downloads (29)
  • HTML views (0)
  • Cited by (4)

[Back to Top]