Reaction-diffusion processes on correlated and uncorrelated scale-free networks

We compare reaction-diffusion processes of the $A+A\to 0$ type on scale-free networks created with either the configuration model or the uncorrelated configuration model. We show via simulations that except for the difference in the behavior of the two models, different results are observed within the same model when the minimum number of connections for a node varies from $k_{\rm min}=1$ to $k_{\rm min}=2$. This difference is attributed to the varying local properties of the two systems. In all cases we are able to identify a power law behavior of the density decay with time with an exponent $f>1$, considerably larger than its lattice counterpart

Scale-free networks resistant to intentional attacks

We study the detailed mechanism of the failure of scale-free networks under intentional attacks. Although it is generally accepted that such networks are very sensitive to targeted attacks, we show that for a particular type of structure such networks surprisingly remain very robust even under removal of a large fraction of their nodes, which in some cases can be up to 70%. The degree distribution $P(k)$ of these structures is such that for small values of the degree $k$ the distribution is constant with $k$, up to a critical value $k_c$, and thereafter it decays with $k$ with the usual power law. We describe in detail a model for such a scale-free network with this modified degree distribution, and we show both analytically and via simulations, that this model can adequately describe all the features and breakdown characteristics of these attacks. We have found several experimental networks with such features, such as for example the IMDB actors collaboration network or the citations network, whose resilience to attacks can be accurately described by our model.Comment: 5 pages, 4 figure

Self-organizing social hierarchies on scale-free networks

In this work we extend the model of Bonabeau et al. in the case of scale-free networks. A sharp transition is observed from an egalitarian to an hierarchical society, with a very low population density threshold. The exact threshold value also depends on the network size. We find that in an hierarchical society the number of individuals with strong winning attitude is much lower than the number of the community members that have a low winning probability

The Effect of Disease-induced Mortality on Structural Network Properties

As the understanding of the importance of social contact networks in the spread of infectious diseases has increased, so has the interest in understanding the feedback process of the disease altering the social network. While many studies have explored the influence of individual epidemiological parameters and/or underlying network topologies on the resulting disease dynamics, we here provide a systematic overview of the interactions between these two influences on population-level disease outcomes. We show that the sensitivity of the population-level disease outcomes to the combination of epidemiological parameters that describe the disease are critically dependent on the topological structure of the population's contact network. We introduce a new metric for assessing disease-driven structural damage to a network as a population-level outcome. Lastly, we discuss how the expected individual-level disease burden is influenced by the complete suite of epidemiological characteristics for the circulating disease and the ongoing process of network compromise. Our results have broad implications for prediction and mitigation of outbreaks in both natural and human populations.Comment: 23 pages, 6 figure

The effect of cities and distance on COVID-19 spreading in the United States

The COVID-19 pandemic has evolved over time through multiple spatial and temporal dynamics. The varying extent of interactions among different geographical areas can result to a complex pattern of spreading so that influences between these areas can be hard to discern. Here, we use cross-correlation analysis to detect synchronous evolution and potential inter-influences in the time evolution of new COVID-19 cases at the county level in the USA. Our analysis identified two main time periods with distinguishable features in the behavior of correlations. In the first phase, there were few strong correlations which only emerged between urban areas. In the second phase of the epidemic, strong correlations became widespread and there was a clear directionality of influence from urban to rural areas. In general, the effect of distance between two counties was much weaker than that of the counties population. Such analysis can provide possible clues on the evolution of the disease and may identify parts of the country where intervention may be more efficient in limiting the disease spread.Comment: 18 pages, 7 figure