Progettazione ed implementazione di strumenti per la valutazione di reti complesse con proprietà scale-free

Il cervello è una rete di cellule nervose connesse da assoni e le cellule stesse sono reti di molecole connesse da reazioni biochimiche. Anche le società sono reti di persone collegate da rapporti di amicizia, parentela e legami professionali. Su più larga scala, catene alimentari ed ecosistemi possono essere rappresentati come reti di specie viventi. E le reti pervadono la tecnologia: Internet, reti elettriche e sistemi di trasporto non sono che pochi degli esempi possibili. Anche il linguaggio che si sta usando in questo momento per veicolare questi ragionamenti a chi legge è una rete, fatta di parole connesse da relazioni sintattiche. A dispetto dell'importanza e della pervasività delle reti, gli scienziati hanno sempre avuto poca comprensione delle loro strutture e proprietà. In che modo le interazioni di alcuni nodi non funzionanti in una complessa rete genetica possono generare il cancro? Come può avvenire così rapidamente la diffusione in taluni sistemi sociali e di comunicazioni, portando ad epidemie di malattie e a virus informatici? Come possono alcune reti continuare a funzionare anche dopo che la maggioranza dei loro nodi ha, invece, smesso di farlo? [...] Le reti reali sono realmente casuali?

Scale-free network of a dengue epidemic

In this work we show that the dengue epidemic in the city of Singapore organized itself into a scale-free network of transmission as the 2000-2005 outbreaks progressed. This scale-free network of cluster comprised geographical breeding places for the aedes mosquitoes, acting as super-spreaders nodes in a network of transmission. The geographical organization of the network was analysed by the corresponding distribution of weekly number of new cases. Therefore, our hypothesis is that the distribution of dengue cases reflects the geographical organization of a transmission network, which evolved towards a power law as the epidemic intensity progressed until 2005. (c) 2007 Elsevier Inc. All rights reserved.

Scale-free networks and scalable interdomain routing

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática

Absence of epidemic threshold in scale free networks with degree correlations

Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide for the susceptible-infected-susceptible model an exact result showing that a scale-free degree distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or disassortative mixing. Degree correlations result therefore irrelevant for the epidemic spreading picture in these scale-free networks. The present result is related to the divergence of the average nearest neighbors degree, enforced by the degree detailed balance condition.

Generation of uncorrelated random scale-free networks

Uncorrelated random scale-free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two- and three-vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k, respectively.

Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations

An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.

Generating Scale-free Networks with Adjustable Clustering Coefficient Via Random Walks

This paper presents an algorithm for generating scale-free networks with adjustable clustering coefficient. The algorithm is based on a random walk procedure combined with a triangle generation scheme which takes into account genetic factors; this way, preferential attachment and clustering control are implemented using only local information. Simulations are presented which support the validity of the scheme, characterizing its tuning capabilities.

Fluctuation-driven traffic congestion in a scale-free model of the Internet

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analysing network failures caused by hardware faults or overload. There network reaction was modelled as rerouting of traffic away from failed or congested elements. Here we model network reaction to congestion on much shorter time scales when the input traffic rate through congested routes is reduced. As an example we consider the Internet where local mismatch between demand and capacity results in traffic losses. We describe the onset of congestion as a phase transition characterised by strong, albeit relatively short-lived, fluctuations of losses caused by noise in input traffic and exacerbated by the heterogeneous nature of the network manifested in a power-law load distribution. The fluctuations may result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible. © 2013 IEEE.

Origin of scale-free intermittency in structural first-order phase transitions

16 pages, 22 figures

Scale-dependent to scale-free: daily behavioural switching and optimized searching in a marine predator

Highlights • We study diel behavioural differences in activity patterns in bigeye tuna. • Daytime activity patterns showed scale free movements consistent with searching. • Night-time activity showed simpler movements indicative of rich patch exploitation. • The results confirm predictions of the Lévy foraging hypothesis.