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Register a new userLimits of Friendship Networks in Predicting Epidemic Risk
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The spread of an infection on a real-world social network is determined by the interplay of two processes: the dynamics of the network, whose structure changes over time according to the encounters between individuals, and the dynamics on the network, whose nodes can infect each other after an encounter. Physical encounter is the most common vehicle for the spread of infectious diseases, but detailed information about encounters is often unavailable because expensive, unpractical to collect or privacy sensitive. We asks whether the friendship ties between the individuals in a social network successfully predict who is at risk. Using a dataset from a popular online review service, we build a time-varying network that is a proxy of physical encounter between users and a static network based on reported friendship. Through computer simulations, we compare infection processes on the resulting networks and show that, whereas distance on the friendship network is correlated to epidemic risk, friendship provides a poor identification of the individuals at risk if the infection is driven by physical encounter. Such limit is not due to the randomness of the infection, but to the structural differences of the two networks. In contrast to the macroscopic similarity between processes spreading on different networks, the differences in local connectivity determined by the two definitions of edges result in striking differences between the dynamics at a microscopic level. Despite the limits highlighted, we show that periodical and relatively infrequent monitoring of the real infection on the encounter network allows to correct the predicted infection on the friendship network and to achieve satisfactory prediction accuracy. In addition, the friendship network contains valuable information to effectively contain epidemic outbreaks when a limited budget is available for immunization.
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Despite the structural properties of online social networks have attracted much attention, the properties of the close-knit friendship structures remain an important question. Here, we mainly focus on how these mesoscale structures are affected by the local and global structural properties. Analyzing the data of four large-scale online social networks reveals several common structural properties. It is found that not only the local structures given by the indegree, outdegree, and reciprocal degree distributions follow a similar scaling behavior, the mesoscale structures represented by the distributions of close-knit friendship structures also exhibit a similar scaling law. The degree correlation is very weak over a wide range of the degrees. We propose a simple directed network model that captures the observed properties. The model incorporates two mechanisms: reciprocation and preferential attachment. Through rate equation analysis of our model, the local-scale and mesoscale structural properties are derived. In the local-scale, the same scaling behavior of indegree and outdegree distributions stems from indegree and outdegree of nodes both growing as the same function of the introduction time, and the reciprocal degree distribution also shows the same power-law due to the linear relationship between the reciprocal degree and in/outdegree of nodes. In the mesoscale, the distributions of four closed triples representing close-knit friendship structures are found to exhibit identical power-laws, a behavior attributed to the negligible degree correlations. Intriguingly, all the power-law exponents of the distributions in the local-scale and mesoscale depend only on one global parameter -- the mean in/outdegree, while both the mean in/outdegree and the reciprocity together determine the ratio of the reciprocal degree of a node to its in/outdegree.
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