-
Previous Article
Graph theory and qualitative analysis of reaction networks
- NHM Home
- This Issue
-
Next Article
Multi-level science mapping with asymmetrical paradigmatic proximity
Augmenting $k$-core generation with preferential attachment
1. | Faculty of Informatics, Universität Karlsruhe (TH), 78131 Karlsruhe, Germany, Germany, Germany, Germany, Germany |
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.
[1] |
José Ignacio Alvarez-Hamelin, Luca Dall'Asta, Alain Barrat, Alessandro Vespignani. K-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases. Networks and Heterogeneous Media, 2008, 3 (2) : 371-393. doi: 10.3934/nhm.2008.3.371 |
[2] |
François Alouges, Sylvain Faure, Jutta Steiner. The vortex core structure inside spherical ferromagnetic particles. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1259-1282. doi: 10.3934/dcds.2010.27.1259 |
[3] |
Magdalena Foryś-Krawiec, Jana Hantáková, Piotr Oprocha. On the structure of α-limit sets of backward trajectories for graph maps. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1435-1463. doi: 10.3934/dcds.2021159 |
[4] |
Maria Aguareles, Marco A. Fontelos, Juan J. Velázquez. The structure of the quiescent core in rigidly rotating spirals in a class of excitable systems. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1605-1638. doi: 10.3934/dcdsb.2012.17.1605 |
[5] |
Zhiwen Zhao. Asymptotic analysis for the electric field concentration with geometry of the core-shell structure. Communications on Pure and Applied Analysis, 2022, 21 (4) : 1109-1137. doi: 10.3934/cpaa.2022012 |
[6] |
Jianqin Zhou, Wanquan Liu, Xifeng Wang. Structure analysis on the k-error linear complexity for 2n-periodic binary sequences. Journal of Industrial and Management Optimization, 2017, 13 (4) : 1743-1757. doi: 10.3934/jimo.2017016 |
[7] |
Yaping Wu, Qian Xu. The existence and structure of large spiky steady states for S-K-T competition systems with cross-diffusion. Discrete and Continuous Dynamical Systems, 2011, 29 (1) : 367-385. doi: 10.3934/dcds.2011.29.367 |
[8] |
Fadoua El Moustaid, Amina Eladdadi, Lafras Uys. Modeling bacterial attachment to surfaces as an early stage of biofilm development. Mathematical Biosciences & Engineering, 2013, 10 (3) : 821-842. doi: 10.3934/mbe.2013.10.821 |
[9] |
Marek Bodnar, Urszula Foryś. Time Delay In Necrotic Core Formation. Mathematical Biosciences & Engineering, 2005, 2 (3) : 461-472. doi: 10.3934/mbe.2005.2.461 |
[10] |
Nikolaz Gourmelon. Generation of homoclinic tangencies by $C^1$-perturbations. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 1-42. doi: 10.3934/dcds.2010.26.1 |
[11] |
Johannes Giannoulis. Transport and generation of macroscopically modulated waves in diatomic chains. Conference Publications, 2011, 2011 (Special) : 485-494. doi: 10.3934/proc.2011.2011.485 |
[12] |
Eric Babson and Dmitry N. Kozlov. Topological obstructions to graph colorings. Electronic Research Announcements, 2003, 9: 61-68. |
[13] |
Oded Schramm. Hyperfinite graph limits. Electronic Research Announcements, 2008, 15: 17-23. doi: 10.3934/era.2008.15.17 |
[14] |
J. William Hoffman. Remarks on the zeta function of a graph. Conference Publications, 2003, 2003 (Special) : 413-422. doi: 10.3934/proc.2003.2003.413 |
[15] |
John Kieffer and En-hui Yang. Ergodic behavior of graph entropy. Electronic Research Announcements, 1997, 3: 11-16. |
[16] |
Roberto De Leo, James A. Yorke. The graph of the logistic map is a tower. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5243-5269. doi: 10.3934/dcds.2021075 |
[17] |
Domingo González, Gamaliel Blé. Core entropy of polynomials with a critical point of maximal order. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 115-130. doi: 10.3934/dcds.2019005 |
[18] |
Madeleine Jotz Lean, Kirill C. H. Mackenzie. Transitive double Lie algebroids via core diagrams. Journal of Geometric Mechanics, 2021, 13 (3) : 403-457. doi: 10.3934/jgm.2021023 |
[19] |
Haixia Liu, Jian-Feng Cai, Yang Wang. Subspace clustering by (k,k)-sparse matrix factorization. Inverse Problems and Imaging, 2017, 11 (3) : 539-551. doi: 10.3934/ipi.2017025 |
[20] |
Roy H. Goodman. NLS bifurcations on the bowtie combinatorial graph and the dumbbell metric graph. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 2203-2232. doi: 10.3934/dcds.2019093 |
2021 Impact Factor: 1.41
Tools
Metrics
Other articles
by authors
[Back to Top]