57 research outputs found
Limited path percolation in complex networks
We study the stability of network communication after removal of
links under the assumption that communication is effective only if the shortest
path between nodes and after removal is shorter than where is the shortest path before removal. For a large
class of networks, we find a new percolation transition at
, where and
is the node degree. Below , only a fraction of
the network nodes can communicate, where , while above , order nodes can
communicate within the limited path length . Our analytical results
are supported by simulations on Erd\H{o}s-R\'{e}nyi and scale-free network
models. We expect our results to influence the design of networks, routing
algorithms, and immunization strategies, where short paths are most relevant.Comment: 11 pages, 3 figures, 1 tabl
Quantum percolation in complex networks
Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2018, Tutor: Marián BoguñáComplex quantum networks will be essential in the future either for the distribution of quantum information (telecommunications) or for studying complex quantical linked systems among others. Complex networks have a wide variety of properties that will help us understand how complex quantum networks behave. Here we will study how this complex networks perform using local quantum transformations at the nodes. We will focus specifcally on the Internet network and we will study its behaviour from a current and quantum perspective
Extended-range percolation in complex networks
Classical percolation theory underlies many processes of information transfer
along the links of a network. In these standard situations, the requirement for
two nodes to be able to communicate is the presence of at least one
uninterrupted path of nodes between them. In a variety of more recent data
transmission protocols, such as the communication of noisy data via
error-correcting repeaters, both in classical and quantum networks, the
requirement of an uninterrupted path is too strict: two nodes may be able to
communicate even if all paths between them have interruptions/gaps consisting
of nodes that may corrupt the message. In such a case a different approach is
needed. We develop the theoretical framework for extended-range percolation in
networks, describing the fundamental connectivity properties relevant to such
models of information transfer. We obtain exact results, for any range , for
infinite random uncorrelated networks and we provide a message-passing
formulation that works well in sparse real-world networks. The interplay of the
extended range and heterogeneity leads to novel critical behavior in scale-free
networks.Comment: 6 pages, 2 figures + Supplementary Materia
A sampling-guided unsupervised learning method to capture percolation in complex networks
The use of machine learning techniques in classical and quantum systems has
led to novel techniques to classify ordered and disordered phases, as well as
uncover transition points in critical phenomena. Efforts to extend these
methods to dynamical processes in complex networks is a field of active
research. Network-percolation, a measure of resilience and robustness to
structural failures, as well as a proxy for spreading processes, has numerous
applications in social, technological, and infrastructural systems. A
particular challenge is to identify the existence of a percolation cluster in a
network in the face of noisy data. Here, we consider bond-percolation, and
introduce a sampling approach that leverages the core-periphery structure of
such networks at a microscopic scale, using onion decomposition, a refined
version of the core. By selecting subsets of nodes in a particular layer of
the onion spectrum that follow similar trajectories in the percolation process,
percolating phases can be distinguished from non-percolating ones through an
unsupervised clustering method. Accuracy in the initial step is essential for
extracting samples with information-rich content, that are subsequently used to
predict the critical transition point through the confusion scheme, a recently
introduced learning method. The method circumvents the difficulty of missing
data or noisy measurements, as it allows for sampling nodes from both the core
and periphery, as well as intermediate layers. We validate the effectiveness of
our sampling strategy on a spectrum of synthetic network topologies, as well as
on two real-word case studies: the integration time of the US domestic airport
network, and the identification of the epidemic cluster of COVID-19 outbreaks
in three major US states. The method proposed here allows for identifying phase
transitions in empirical time-varying networks.Comment: 16 pages, 6 figure
How does bond percolation happen in coloured networks?
Percolation in complex networks is viewed as both: a process that mimics
network degradation and a tool that reveals peculiarities of the underlying
network structure. During the course of percolation, networks undergo
non-trivial transformations that include a phase transition in the
connectivity, and in some special cases, multiple phase transitions. Here we
establish a generic analytic theory that describes how structure and sizes of
all connected components in the network are affected by simple and
colour-dependant bond percolations. This theory predicts all locations where
the phase transitions take place, existence of wide critical windows that do
not vanish in the thermodynamic limit, and a peculiar phenomenon of colour
switching that occurs in small connected components. These results may be used
to design percolation-like processes with desired properties, optimise network
response to percolation, and detect subtle signals that provide an early
warning of a network collapse
Coupled effects of local movement and global interaction on contagion
By incorporating segregated spatial domain and individual-based linkage into
the SIS (susceptible-infected-susceptible) model, we investigate the coupled
effects of random walk and intragroup interaction on contagion. Compared with
the situation where only local movement or individual-based linkage exists, the
coexistence of them leads to a wider spread of infectious disease. The roles of
narrowing segregated spatial domain and reducing mobility in epidemic control
are checked, these two measures are found to be conducive to curbing the spread
of infectious disease. Considering heterogeneous time scales between local
movement and global interaction, a log-log relation between the change in the
number of infected individuals and the timescale is found. A theoretical
analysis indicates that the evolutionary dynamics in the present model is
related to the encounter probability and the encounter time. A functional
relation between the epidemic threshold and the ratio of shortcuts, and a
functional relation between the encounter time and the timescale are
found
k-core organization of complex networks
We analytically describe the architecture of randomly damaged uncorrelated
networks as a set of successively enclosed substructures -- k-cores. The k-core
is the largest subgraph where vertices have at least k interconnections. We
find the structure of k-cores, their sizes, and their birth points -- the
bootstrap percolation thresholds. We show that in networks with a finite mean
number z_2 of the second-nearest neighbors, the emergence of a k-core is a
hybrid phase transition. In contrast, if z_2 diverges, the networks contain an
infinite sequence of k-cores which are ultra-robust against random damage.Comment: 5 pages, 3 figure
Hierarchical scale-free network is fragile against random failure
We investigate site percolation in a hierarchical scale-free network known as
the Dorogovtsev- Goltsev-Mendes network. We use the generating function method
to show that the percolation threshold is 1, i.e., the system is not in the
percolating phase when the occupation probability is less than 1. The present
result is contrasted to bond percolation in the same network of which the
percolation threshold is zero. We also show that the percolation threshold of
intentional attacks is 1. Our results suggest that this hierarchical scale-free
network is very fragile against both random failure and intentional attacks.
Such a structural defect is common in many hierarchical network models.Comment: 11 pages, 4 figure
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