Complex Networks: a Mini-review
TL;DR: A brief review about complex networks including fundamental quantities, examples of network models, and the essential role of network topology in the investigation of dynamical processes as epidemics, rumor spreading, and synchronization is presented.
Abstract: Network analysis is a powerful tool that provides us a fruitful framework to describe phenomena related to social, technological, and many other real-world complex systems. In this paper, we present a brief review about complex networks including fundamental quantities, examples of network models, and the essential role of network topology in the investigation of dynamical processes as epidemics, rumor spreading, and synchronization. A quite of advances have been provided in this field, and many other authors also review the main contributions in this area over the years. However, we show an overview from a different perspective. Our aim is to provide basic information to a broad audience and more detailed references for those who would like to learn deeper the topic.
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TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.
7,116 citations
Book•
19 Nov 2012
TL;DR: This chapter describes the origin and evolution of systems biology, as a formal discipline, steps and challenges in building models and their potential applications.
Abstract: In the mid 1990s when Leroy Hood reintroduced the term “Systems Biology”, the fusion of ideas gave rise to confusion to such an extent that there used to be special talks on ‘what is systems biology’? Over the last decade, Systems Biology has undergone directed evolution leading to the emergence of personalized versions of this term. Irrespective of this, strong computational dependency and a significant increase in the scale of investigation often appear as constant features in the systems biology background. In our opinion, Systems Biology is an approach that involves the following (a) experimental and computational studies describing collective behavior of molecules in relation to the pathway and networks, and with the higher-level physiological outcome (b) new experimental and mathematical methods important to study group behavior of interacting components. This chapter describes the origin and evolution of systems biology, as a formal discipline, steps and challenges in building models and their potential applications.
21 citations
TL;DR: In this paper, the authors performed a systematic performance analysis in well-known dynamics and topologies and found that all learning curves displayed the same learning shape, with different speed rates, and ambiguities in the feature space describing the learning curves, meaning that the same knowledge acquisition curve can be generated in different combinations of network topology and dynamics.
9 citations
TL;DR: A new node attack strategy removing nodes with the highest conditional weighted betweenness centrality (CondWBet) is introduced, which combines the weighted structure of the network and the node’s conditional betweenness and is found to be the most effective strategy to reduce WEFF in 3 out of 5 cases.
Abstract: In this work, we introduce a new node attack strategy removing nodes with the highest conditional weighted betweenness centrality (CondWBet), which combines the weighted structure of the network and the node’s conditional betweenness. We compare its efficacy with well-known attack strategies from literature over five real-world complex weighted networks. We use the network weighted efficiency (WEFF) like a measure encompassing the weighted structure of the network, in addition to the commonly used binary-topological measure, i.e., the largest connected cluster (LCC). We find that if the measure is WEFF, the CondWBet strategy is the best to decrease WEFF in 3 out of 5 cases. Further, CondWBet is the most effective strategy to reduce WEFF at the beginning of the removal process, whereas the Strength that removes nodes with the highest sum of the link weights first shows the highest efficacy in the final phase of the removal process when the network is broken into many small clusters. These last outcomes would suggest that a better attacking in weighted networks strategy could be a combination of the CondWBet and Strength strategies.
7 citations
Cites background from "Complex Networks: a Mini-review"
...*e study of real-world complex networks has attractedmuch attention in recent decades because a large number of real complex systems can be abstracted as networks [1, 2]....
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TL;DR: In this article , a systematic review of critical infrastructure resilience under compounding/cascading threats was conducted, which indicated that literature has focused on absorption of compounding and cascading threats by critical infrastructure, particularly within the physical and information domains.
Abstract: Multiple threat events may disrupt critical infrastructure functioning, thereby inhibiting the provision of essential goods and services to affected communities. It is currently unclear how modeling approaches have assessed critical infrastructure resilience when facing compounding (i.e., the COVID-19 pandemic co-occurring with natural hazards) or cascading (i.e., landslides following wildland fires) threats. For both, connection across multiple domains of critical infrastructure are of crucial importance and modeling risk and resilience associated with complex threats has been proposed as a way forward in assessing and managing systemic risk and resilience. A systematic review is conducted to understand how critical infrastructure resilience was assessed in network science literature published between 2010 and 2021. The literature was classified based on phases of resilience (preparation, absorption, recovery, and adaptation) and system domains (physical, information, cognitive, social). Results indicate that literature has focused on absorption of compounding and cascading threats by critical infrastructure, particularly within the physical and information domains. Results also identified a potential gap in network science models' incorporation of the resilience phases of preparation and adaption, signifying a potential opportunity for network science methodologies to integrate all four phases into models of critical infrastructure resilience. • Review of critical infrastructure resilience under compounding/cascading threats was conducted. • Used the Resilience Matrix approach to codify literature. • Results showed emphases on absorption and recovery, lack of preparation and adaptation integration. • Additional emphases on physical and information resilience domains, lack of cognitive and social domains. • Models that used a resilience-based framework generally covered the Resilience Matrix more comprehensively.
7 citations
References
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TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
39,297 citations
TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Abstract: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
33,771 citations
"Complex Networks: a Mini-review" refers background in this paper
...Concomitantly, Barabási and Albert [46] proposed a preferential attachment model suited to reproduce the feature of time growth of many real networks....
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...Concomitantly, Barabási and Albert [46] proposed a preferential attachment model suited to reproduce the feature of time growth of many real networks....
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...The Barabasi-Albert model does not take into account that nodes can have other attributes that make them more attractive to receive new links....
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...If we take αA = 0, we return to the well-known Barabasi-Albert model....
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TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
Abstract: The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them.
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other.
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.
18,415 citations
Journal Article•
TL;DR: Google as discussed by the authors is a prototype of a large-scale search engine which makes heavy use of the structure present in hypertext and is designed to crawl and index the Web efficiently and produce much more satisfying search results than existing systems.
13,327 citations
Book•
25 Mar 2010
TL;DR: This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.
Abstract: The scientific study of networks, including computer networks, social networks, and biological networks, has received an enormous amount of interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas. Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.
10,567 citations