12 research outputs found
Percolation in self-similar networks
We provide a simple proof that graphs in a general class of self-similar
networks have zero percolation threshold. The considered self-similar networks
include random scale-free graphs with given expected node degrees and zero
clustering, scale-free graphs with finite clustering and metric structure,
growing scale-free networks, and many real networks. The proof and the
derivation of the giant component size do not require the assumption that
networks are treelike. Our results rely only on the observation that
self-similar networks possess a hierarchy of nested subgraphs whose average
degree grows with their depth in the hierarchy. We conjecture that this
property is pivotal for percolation in networks.Comment: 4 pages, 3 figure
Cosmological networks
Networks often represent systems that do not have a long history of study in traditional fields of physics; albeit, there are some notable exceptions, such as energy landscapes and quantum gravity. Here, we consider networks that naturally arise in cosmology. Nodes in these networks are stationary observers uniformly distributed in an expanding open Friedmann-Lemaitre-Robertson-Walker universe with any scale factor and two observers are connected if one can causally influence the other. We show that these networks are growing Lorentz-invariant graphs with power-law distributions of node degrees. These networks encode maximum information about the observable universe available to a given observer
Non-Markovian epidemic spreading on temporal networks
Many empirical studies have revealed that the occurrences of contacts
associated with human activities are non-Markovian temporal processes with a
heavy tailed inter-event time distribution. Besides, there has been increasing
empirical evidence that the infection and recovery rates are time-dependent.
However, we lack a comprehensive framework to analyze and understand
non-Markovian contact and spreading processes on temporal networks. In this
paper, we propose a general formalism to study non-Markovian dynamics on
non-Markovian temporal networks. We find that, under certain conditions,
non-Markovian dynamics on temporal networks are equivalent to Markovian
dynamics on static networks. Interestingly, this result is independent of the
underlying network topology
A Community-Structure-Based Method for Estimating the Fractal Dimension, and its Application to Water Networks for the Assessment of Vulnerability to Disasters
Most real-world networks, from the World-Wide-Web to biological systems, are known to have common structural properties. A remarkable point is fractality, which suggests the self-similarity across scales of the network structure of these complex systems. Managing the computational complexity for detecting the self-similarity of big-sized systems represents a crucial problem. In this paper, a novel algorithm for revealing the fractality, that exploits the community structure principle, is proposed and then applied to several water distribution systems (WDSs) of different size, unveiling a self-similar feature of their layouts. A scaling-law relationship, linking the number of clusters necessary for covering the network and their average size is defined, the exponent of which represents the fractal dimension. The self-similarity is then investigated as a proxy of recurrent and specific response to multiple random pipe failures – like during natural disasters – pointing out a specific global vulnerability for each WDS. A novel vulnerability index, called Cut-Vulnerability is introduced as the ratio between the fractal dimension and the average node degree, and its relationships with the number of randomly removed pipes necessary to disconnect the network and with some topological metrics are investigated. The analysis shows the effectiveness of the novel index in describing the global vulnerability of WDSs
A Community-Structure-Based Method for Estimating the Fractal Dimension, and its Application to Water Networks for the Assessment of Vulnerability to Disasters
AbstractMost real-world networks, from the World-Wide-Web to biological systems, are known to have common structural properties. A remarkable point is fractality, which suggests the self-similarity across scales of the network structure of these complex systems. Managing the computational complexity for detecting the self-similarity of big-sized systems represents a crucial problem. In this paper, a novel algorithm for revealing the fractality, that exploits the community structure principle, is proposed and then applied to several water distribution systems (WDSs) of different size, unveiling a self-similar feature of their layouts. A scaling-law relationship, linking the number of clusters necessary for covering the network and their average size is defined, the exponent of which represents the fractal dimension. The self-similarity is then investigated as a proxy of recurrent and specific response to multiple random pipe failures – like during natural disasters – pointing out a specific global vulnerability for each WDS. A novel vulnerability index, called Cut-Vulnerability is introduced as the ratio between the fractal dimension and the average node degree, and its relationships with the number of randomly removed pipes necessary to disconnect the network and with some topological metrics are investigated. The analysis shows the effectiveness of the novel index in describing the global vulnerability of WDSs
Self-similar scaling of density in complex real-world networks
Despite their diverse origin, networks of large real-world systems reveal a
number of common properties including small-world phenomena, scale-free degree
distributions and modularity. Recently, network self-similarity as a natural
outcome of the evolution of real-world systems has also attracted much
attention within the physics literature. Here we investigate the scaling of
density in complex networks under two classical box-covering
renormalizations-network coarse-graining-and also different community-based
renormalizations. The analysis on over 50 real-world networks reveals a
power-law scaling of network density and size under adequate renormalization
technique, yet irrespective of network type and origin. The results thus
advance a recent discovery of a universal scaling of density among different
real-world networks [Laurienti et al., Physica A 390 (20) (2011) 3608-3613.]
and imply an existence of a scale-free density also within-among different
self-similar scales of-complex real-world networks. The latter further improves
the comprehension of self-similar structure in large real-world networks with
several possible applications
Critical behavior and correlations on scale-free small-world networks: Application to network design
We analyze critical phenomena on networks generated as the union of hidden variable models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small worlds similar to those a la Watts and Strogatz, but with a heterogeneous degree distribution. We prove that the critical behavior (thermal or percolative) remains completely unchanged by the presence of finite loops (or finite clustering). Then, we show that, in large but finite networks, correlations of two given spins may be strong, i.e., approximately power-law-like, at any temperature. Quite interestingly, if gamma is the exponent for the power-law distribution of the vertex degree, for gamma <= 3 and with or without short-range couplings, such strong correlations persist even in the thermodynamic limit, contradicting the common opinion that, in mean-field models, correlations always disappear in this limit. Finally, we provide the optimal choice of rewiring under which percolation phenomena in the rewired network are best performed, a natural criterion to reach best communication features, at least in noncongested regimes.PTDC/FIS/108476/2008,PTDC/MAT/114515/2009SOCIALNET
The hidden hyperbolic geometry of international trade: World Trade Atlas 1870-2013
Here, we present the World Trade Atlas 1870-2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, based on a gravity model predicting the existence of significant trade channels, are such that the closer countries are in trade space, the greater their chance of becoming connected. The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat but hyperbolic, as a reflection of its complex architecture. The departure from flatness has been increasing since World War I, meaning that differences in trade distances are growing and trade networks are becoming more hierarchical. Smaller-scale economies are moving away from other countries except for the largest economies; meanwhile those large economies are increasing their chances of becoming connected worldwide. At the same time, Preferential Trade Agreements do not fit in perfectly with natural communities within the trade space and have not necessarily reduced internal trade barriers. We discuss an interpretation in terms of globalization, hierarchization, and localization; three simultaneous forces that shape the international trade system