1,721,049 research outputs found
How the science of complex networks can help developing strategies against terrorism
Get PDFA new method, based on a recently defined centrality measure, allows to spot the critical components of a generic complex network. The identification and protection of the critical components of a given communication–transportation network should be the first concern in order to reduce the consequences of terrorist attacks. On the other hand, the critical components of a terrorist organization are the terrorists to target to disrupt the organization and reduce the possibility of terroristic attacks
Is the Boston subway a small-world network?
No full textThe mathematical study of the small-world concept has fostered quite some interest, showing that small-world features can be identified for some abstract classes of networks. However, passing to real complex systems, as for instance transportation networks, shows a number of new problems that make current analysis impossible. In this paper we show how a more refined kind of analysis, relying on transportation efficiency, can in fact be used to overcome such problems, and to give precious insights on the general characteristics of real transportation networks, eventually providing a picture where the small-world comes back as underlying construction principle
Economic small-world behavior in weighted networks
No full textThe small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation is valid only for topological networks. In this paper we propose a generalization of the theory of small worlds based on two leading concepts, efficiency and cost, and valid also for weighted networks. Efficiency measures how well information propagates over the network, and cost measures how expensive it is to build a network. The combination of these factors leads us to introduce the concept of economic small worlds, that formalizes the idea of networks that are “cheap” to build, and nevertheless efficient in propagating information, both at global and local scale. In this way we provide an adequate tool to quantitatively analyze the behaviour of complex networks in the real world. Various complex systems are studied, ranging from the realm of neural networks, to social sciences, to communication and transportation networks. In each case, economic small worlds are found. Moreover, using the economic small-world framework, the construction principles of these networks can be quantitatively analyzed and compared, giving good insights on how efficiency and economy principles combine up to shape all these systems
The architecture of complex systems
No full textIn the last few years the research on networks has taken different directions
producing rather unexpected and important results. Researchers have: 1)
proposed various global variables to describe and characterize the properties of real-world networks; 2) developed different models to simulate the formation and the growth of networks as the ones found in the real world. The results obtained can be summed up by saying that statistical physics has been able to capture the structure of many diverse systems within a few common frameworks, though these common frameworks are very dierent from the regular array, or the random connectivity, previously used to model the network of a complex system.
Here we present a list of some of the global quantities introduced to characterize a network: the characteristic path length L, the clustering coefficient C, the global efficiency Eglob, the local efficiency Eloc, the cost Cost, and the degree distribution P(k).We also review two classes of networks proposed: smallworld and scale-free networks. We conclude with a possible application of the nonextensive thermodynamics formalism to describe scale-free networks
Extended-range percolation and complex networks
Get PDFThis PhD thesis investigates percolation in complex networks, focusing on a novel model called extended-range percolation. This model is studied on various complex structures, with an exact solution provided using generating functions and message-passing techniques. Additionally, a novel model for highly-clustered random graphs is presented and analyzed both numerically and analytically.
The thesis begins by introducing basic concepts of percolation theory and provides a comprehensive review of critical properties on uncorrelated locally tree-like random graphs. It aims to bridge gaps in existing literature by offering a unified framework for understanding percolation's critical properties.
The second part of the thesis discusses extended-range percolation, where inactive nodes do not disrupt connectivity within a defined interaction range R. An exact solution is presented using generating functions and mean-field-like recursive equations, revealing non-universal behavior in strongly heterogeneous networks. A message-passing framework is developed to analyze extended-range percolation on tree-like networks for arbitrary R, and its application to multiplex networks is explored, leading to novel percolation critical phenomena.
In the third part, a model for highly-clustered random graphs is introduced by closing open triads in uncorrelated random graphs. This allows for the exact computation of topological properties and provides insights into how clustering affects percolation critical exponents.
Finally, a brief summary of a parallel project on optimizing quantum communication networks is presented, demonstrating practical applications of theoretical findings.
This thesis advances the understanding of percolation processes in complex networks through innovative models, contributing valuable insights into communication systems and other fields influenced by network theory. These findings pave the way for future research directions that could further explore the applications of percolation theory in various contexts
A topological analysis of the Italian electric power grid
No full textLarge-scale blackouts are an intrinsic drawback of electric power transmission grids. Here we analyze the structural vulnerability of the Italian GRTN power grid by using a model for cascading failures recently proposed in Crucitti et al. (Phys. Rev. E 69 (2004))
Efficient behavior of small-world networks
Get PDFWe introduce the concept of efficiency of a network as a measure of how efficiently it exchanges information. By using this simple measure, small-world networks are seen as systems that are both globally and locally efficient. This gives a clear physical meaning to the concept of “small world,” and also a precise quantitative analysis of both weighted and unweighted networks. We study neural networks and man-made communication and transportation systems and we show that the underlying general principle of their construction is in fact a small-world principle of high efficiency
Harmony in the small-world
No full textThe small-world phenomenon, popularly known as six degrees of separation, has been mathematically formalized by Watts and Strogatz in a study of the topological properties of a network. Small-world networks are defined in terms of two quantities: they have a high clustering coefficient C like regular lattices and a short characteristic path length L typical of random networks. Physical distances are of fundamental importance in applications to real cases; nevertheless, this basic ingredient is missing in the original formulation. Here, we introduce a new concept, the connectivity length D, that gives harmony to the whole theory. D can be evaluated on a global and on a local scale and plays in turn the role of L and 1/C. Moreover, it can be computed for any metrical network and not only for the topological cases. D has a precise meaning in terms of information propagation and describes in a unified way, both the structural and the dynamical aspects of a network: small-worlds are defined by a small global and local D, i.e., by a high efficiency in propagating information both on a local and global scale. The neural system of the nematode C. elegans, the collaboration graph of film actors, and the oldest US subway system, can now be studied also as metrical networks and are shown to be small-worlds
Efficiency of scale-free networks: error and attack tolerance
No full textThe concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e., networks with power law P(k), are considered: (1) scale-free networks with no local clustering produced by the Barabasi–Albert model and (2) scale-free networks with high clustering properties as in the model by Klemm and Eguı́luz, and their properties are compared to the properties of random graphs (exponential graphs). By using as mathematical measures the global and the local efficiency we investigate the effects of errors and attacks both on the global and the local properties of the network. We show that the global efficiency is a better measure than the characteristic path length to describe the response of complex networks to external factors. We find that, at variance with random graphs, scale-free networks display, both on a global and on a local scale, a high degree of error tolerance and an extreme vulnerability to attacks. In fact, the global and the local efficiency are unaffected by the failure of some randomly chosen nodes, though they are extremely sensitive to the removal of the few nodes which play a crucial role in maintaining the network's connectivity
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