Generalised Sandpile Dynamics on Artificial and Real-World Directed Networks
File(s)
Author(s)
Zachariou, N
Expert, P
Takayasu, M
Christensen, K
Type
Journal Article
Abstract
The main finding of this paper is a novel avalanche-size exponent τ 1.87 when the generalised
sandpile dynamics evolves on the real-world Japanese inter-firm network. The topology
of this network is non-layered and directed, displaying the typical bow tie structure
found in real-world directed networks, with cycles and triangles. We show that one can
move from a strictly layered regular lattice to a more fluid structure of the inter-firm network
in a few simple steps. Relaxing the regular lattice structure by introducing an interlayer distribution
for the interactions, forces the scaling exponent of the avalanche-size probability
density function τ out of the two-dimensional directed sandpile universality class τ = 4/3,
into the mean field universality class τ = 3/2. Numerical investigation shows that these two
classes are the only that exist on the directed sandpile, regardless of the underlying topology,
as long as it is strictly layered. Randomly adding a small proportion of links connecting
non adjacent layers in an otherwise layered network takes the system out of the mean field
regime to produce non-trivial avalanche-size probability density function. Although these do
not display proper scaling, they closely reproduce the behaviour observed on the Japanese
inter-firm network.
sandpile dynamics evolves on the real-world Japanese inter-firm network. The topology
of this network is non-layered and directed, displaying the typical bow tie structure
found in real-world directed networks, with cycles and triangles. We show that one can
move from a strictly layered regular lattice to a more fluid structure of the inter-firm network
in a few simple steps. Relaxing the regular lattice structure by introducing an interlayer distribution
for the interactions, forces the scaling exponent of the avalanche-size probability
density function τ out of the two-dimensional directed sandpile universality class τ = 4/3,
into the mean field universality class τ = 3/2. Numerical investigation shows that these two
classes are the only that exist on the directed sandpile, regardless of the underlying topology,
as long as it is strictly layered. Randomly adding a small proportion of links connecting
non adjacent layers in an otherwise layered network takes the system out of the mean field
regime to produce non-trivial avalanche-size probability density function. Although these do
not display proper scaling, they closely reproduce the behaviour observed on the Japanese
inter-firm network.
Date Issued
2015-11-25
Date Acceptance
2015-10-26
Citation
PLOS One, 2015, 10 (11)
ISSN
1932-6203
Publisher
Public Library of Science
Journal / Book Title
PLOS One
Volume
10
Issue
11
Copyright Statement
© 2015 Zachariou et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are
credite
access article distributed under the terms of the
Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are
credite
License URL
Subjects
Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
SELF-ORGANIZED CRITICALITY
SCALE-FREE NETWORKS
AVALANCHE DYNAMICS
COMPLEX NETWORKS
MODEL
EXTREMALITY
BEHAVIOR
POWER
Publication Status
Published
Article Number
e0142685