Although the many forms of modern social media have become major channels for the dissemination of information, they are becoming overloaded because of the rapidly-expanding number of information feeds. We analyze the expanding user-generated content
in Sina Weibo, the largest micro-blog site in China, and find evidence that popular messages often follow a mechanism that differs from that found in the spread of disease, in contrast to common believe. In this mechanism, an individual with more friends needs more repeated exposures to spread further the information. Moreover, our data suggest that in contrast to epidemics, for certain messages the chance of an individual to share the message is proportional to the fraction of its neighbours who shared it with him/her. Thus the greater the number of friends an individual has the greater the number of repeated contacts needed to spread the message, which is a result of competition for attention. We model this process using a fractional susceptible infected recovered (FSIR) model, where the infection probability of a node is proportional to its fraction of infected neighbors. Our findings have dramatic implications for information contagion. For example, using the FSIR model we find that real-world social networks have a finite epidemic threshold. This is in contrast to the zero threshold that conventional wisdom derives from disease epidemic models. This means that when individuals are overloaded with excess information feeds, the information either reaches out the population if it is above the critical epidemic threshold, or it would never be well received, leading to only a handful of information contents that can be widely spread throughout the population.
Many models of market dynamics make use of the idea of conservative wealth exchanges among economic agents. A few years ago an exchange model using extremal dynamics was developed and a very interesting result was obtained: a self-generated minimum w
ealth or poverty line. On the other hand, the wealth distribution exhibited an exponential shape as a function of the square of the wealth. These results have been obtained both considering exchanges between nearest neighbors or in a mean field scheme. In the present paper we study the effect of distributing the agents on a complex network. We have considered archetypical complex networks: Erd{o}s-Renyi random networks and scale-free networks. The presence of a poverty line with finite wealth is preserved but spatial correlations are important, particularly between the degree of the node and the wealth. We present a detailed study of the correlations, as well as the changes in the Gini coefficient, that measures the inequality, as a function of the type and average degree of the considered networks.
We consider the discrete surface growth process with relaxation to the minimum [F. Family, J. Phys. A {bf 19} L441, (1986).] as a possible synchronization mechanism on scale-free networks, characterized by a degree distribution $P(k) sim k^{-lambda}$
, where $k$ is the degree of a node and $lambda$ his broadness, and compare it with the usually applied Edward-Wilkinson process [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London Ser. A {bf 381},17 (1982) ]. In spite of both processes belong to the same universality class for Euclidean lattices, in this work we demonstrate that for scale-free networks with exponents $lambda<3$ this is not true. Moreover, we show that for these ubiquitous cases the Edward-Wilkinson process enhances spontaneously the synchronization when the system size is increased, which is a non-physical result. Contrarily, the discrete surface growth process do not present this flaw and is applicable for every $lambda$.
