9,332 research outputs found
Robustness of Network of Networks with Interdependent and Interconnected links
Robustness of network of networks (NON) has been studied only for dependency
coupling (J.X. Gao et. al., Nature Physics, 2012) and only for connectivity
coupling (E.A. Leicht and R.M. D Souza, arxiv:0907.0894). The case of network
of n networks with both interdependent and interconnected links is more
complicated, and also more closely to real-life coupled network systems. Here
we develop a framework to study analytically and numerically the robustness of
this system. For the case of starlike network of n ER networks, we find that
the system undergoes from second order to first order phase transition as
coupling strength q increases. We find that increasing intra-connectivity links
or inter-connectivity links can increase the robustness of the system, while
the interdependency links decrease its robustness. Especially when q=1, we find
exact analytical solutions of the giant component and the first order
transition point. Understanding the robustness of network of networks with
interdependent and interconnected links is helpful to design resilient
infrastructures
Towards designing robust coupled networks
Natural and technological interdependent systems have been shown to be highly
vulnerable due to cascading failures and an abrupt collapse of global
connectivity under initial failure. Mitigating the risk by partial
disconnection endangers their functionality. Here we propose a systematic
strategy of selecting a minimum number of autonomous nodes that guarantee a
smooth transition in robustness. Our method which is based on betweenness is
tested on various examples including the famous 2003 electrical blackout of
Italy. We show that, with this strategy, the necessary number of autonomous
nodes can be reduced by a factor of five compared to a random choice. We also
find that the transition to abrupt collapse follows tricritical scaling
characterized by a set of exponents which is independent on the protection
strategy
Structural transition in interdependent networks with regular interconnections
Networks are often made up of several layers that exhibit diverse degrees of
interdependencies. A multilayer interdependent network consists of a set of
graphs that are interconnected through a weighted interconnection matrix , where the weight of each inter-graph link is a non-negative real number . Various dynamical processes, such as synchronization, cascading failures
in power grids, and diffusion processes, are described by the Laplacian matrix
characterizing the whole system. For the case in which the multilayer
graph is a multiplex, where the number of nodes in each layer is the same and
the interconnection matrix , being the identity matrix, it has
been shown that there exists a structural transition at some critical coupling,
. This transition is such that dynamical processes are separated into
two regimes: if , the network acts as a whole; whereas when , the network operates as if the graphs encoding the layers were isolated. In
this paper, we extend and generalize the structural transition threshold to a regular interconnection matrix (constant row and column sum).
Specifically, we provide upper and lower bounds for the transition threshold in interdependent networks with a regular interconnection matrix
and derive the exact transition threshold for special scenarios using the
formalism of quotient graphs. Additionally, we discuss the physical meaning of
the transition threshold in terms of the minimum cut and show, through
a counter-example, that the structural transition does not always exist. Our
results are one step forward on the characterization of more realistic
multilayer networks and might be relevant for systems that deviate from the
topological constrains imposed by multiplex networks.Comment: 13 pages, APS format. Submitted for publicatio
Towards real-world complexity: an introduction to multiplex networks
Many real-world complex systems are best modeled by multiplex networks of
interacting network layers. The multiplex network study is one of the newest
and hottest themes in the statistical physics of complex networks. Pioneering
studies have proven that the multiplexity has broad impact on the system's
structure and function. In this Colloquium paper, we present an organized
review of the growing body of current literature on multiplex networks by
categorizing existing studies broadly according to the type of layer coupling
in the problem. Major recent advances in the field are surveyed and some
outstanding open challenges and future perspectives will be proposed.Comment: 20 pages, 10 figure
Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review
Infrastructure systems, such as power, transportation, telecommunication, and water systems, are composed of multiple components which are interconnected and interdependent to produce and distribute essential goods and services. So, the robustness of infrastructure systems to resist disturbances is crucial for the durable performance of modern societies. Multilayer networks have been used to model the multiplicity and interrelation of infrastructure systems and percolation theory is the most common approach to quantify the robustness of such networks. This survey systematically reviews literature published between 2010 and 2021, on applying percolation theory to assess the robustness of infrastructure systems modeled as multilayer networks. We discussed all network properties applied to build infrastructure models. Among all properties, interdependency strength and communities were the most common network property whilst very few studies considered realistic attributes of infrastructure systems such as directed links and feedback conditions. The review highlights that the properties produced approximately similar model outcomes, in terms of detecting improvement or deterioration in the robustness of multilayer infrastructure networks, with few exceptions. Most of the studies focused on highly simplified synthetic models rather than models built by real datasets. Thus, this review suggests analyzing multiple properties in a single model to assess whether they boost or weaken the impact of each other. In addition, the effect size of different properties on the robustness of infrastructure systems should be quantified. It can support the design and planning of robust infrastructure systems by arranging and prioritizing the most effective properties
Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review
Infrastructure systems, such as power, transportation, telecommunication, and water systems, are composed of multiple components which are interconnected and interdependent to produce and distribute essential goods and services. So, the robustness of infrastructure systems to resist disturbances is crucial for the durable performance of modern societies. Multilayer networks have been used to model the multiplicity and interrelation of infrastructure systems and percolation theory is the most common approach to quantify the robustness of such networks. This survey systematically reviews literature published between 2010 and 2021, on applying percolation theory to assess the robustness of infrastructure systems modeled as multilayer networks. We discussed all network properties applied to build infrastructure models. Among all properties, interdependency strength and communities were the most common network property whilst very few studies considered realistic attributes of infrastructure systems such as directed links and feedback conditions. The review highlights that the properties produced approximately similar model outcomes, in terms of detecting improvement or deterioration in the robustness of multilayer infrastructure networks, with few exceptions. Most of the studies focused on highly simplified synthetic models rather than models built by real datasets. Thus, this review suggests analyzing multiple properties in a single model to assess whether they boost or weaken the impact of each other. In addition, the effect size of different properties on the robustness of infrastructure systems should be quantified. It can support the design and planning of robust infrastructure systems by arranging and prioritizing the most effective properties
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