Abstract
We study avalanche dynamics on scale-free networks, following a power-law degree distribution, pd(k) ∼ kθ, through the Bak-Tang-Wiesenfeld sandpile model. The threshold height of a node i is set to be ki 1-η with 0≤η<1. We obtain the exponents for the avalanche size and the duration distributions analytically as a function of γ and η by using the branching process approach. The analytic solution is checked with numerical simulations on both artificial uncorrelated networks such as the static model and real-world networks. While numerical results of the avalanche size distribution for artificial uncorrelated scale-free networks are in reasonable agreement with the analytic prediction, those for real-world networks are not, which may be attributed to non-trivial degree-degree correlations in real-world networks.
| Original language | English |
|---|---|
| Pages (from-to) | 93-103 |
| Number of pages | 11 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 346 |
| Issue number | 1-2 SPEC. ISS. |
| DOIs | |
| Publication status | Published - 2005 Feb 1 |
| Externally published | Yes |
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Keywords
- Avalanche
- Branching process
- Scale-free network
ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics
Cite this
Cascading toppling dynamics on scale-free networks. / Goh, Kwang-Il; Lee, D. S.; Kahng, B.; Kim, D.
In: Physica A: Statistical Mechanics and its Applications, Vol. 346, No. 1-2 SPEC. ISS., 01.02.2005, p. 93-103.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Cascading toppling dynamics on scale-free networks
AU - Goh, Kwang-Il
AU - Lee, D. S.
AU - Kahng, B.
AU - Kim, D.
PY - 2005/2/1
Y1 - 2005/2/1
N2 - We study avalanche dynamics on scale-free networks, following a power-law degree distribution, pd(k) ∼ kθ, through the Bak-Tang-Wiesenfeld sandpile model. The threshold height of a node i is set to be ki 1-η with 0≤η<1. We obtain the exponents for the avalanche size and the duration distributions analytically as a function of γ and η by using the branching process approach. The analytic solution is checked with numerical simulations on both artificial uncorrelated networks such as the static model and real-world networks. While numerical results of the avalanche size distribution for artificial uncorrelated scale-free networks are in reasonable agreement with the analytic prediction, those for real-world networks are not, which may be attributed to non-trivial degree-degree correlations in real-world networks.
AB - We study avalanche dynamics on scale-free networks, following a power-law degree distribution, pd(k) ∼ kθ, through the Bak-Tang-Wiesenfeld sandpile model. The threshold height of a node i is set to be ki 1-η with 0≤η<1. We obtain the exponents for the avalanche size and the duration distributions analytically as a function of γ and η by using the branching process approach. The analytic solution is checked with numerical simulations on both artificial uncorrelated networks such as the static model and real-world networks. While numerical results of the avalanche size distribution for artificial uncorrelated scale-free networks are in reasonable agreement with the analytic prediction, those for real-world networks are not, which may be attributed to non-trivial degree-degree correlations in real-world networks.
KW - Avalanche
KW - Branching process
KW - Scale-free network
UR - http://www.scopus.com/inward/record.url?scp=10044223608&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=10044223608&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2004.08.054
DO - 10.1016/j.physa.2004.08.054
M3 - Article
AN - SCOPUS:10044223608
VL - 346
SP - 93
EP - 103
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
IS - 1-2 SPEC. ISS.
ER -