"Contacts between individuals serve as pathways where infections may propagate. These contact patterns can be represented by network structures. Static structures have been the common modeling paradigm but recent results suggest that temporal structures play different roles to regulate the spread of infections or infection-like dynamics. On temporal networks a vertex is active only at certain moments and inactive otherwise such that a contact is not continuously available. In several empirical networks, the time between two consecutive vertex-activation events typically follows heterogeneous activity (e.g. bursts). In this chapter, we present a simple and intuitive stochastic model of a temporal network and investigate how epidemics co-evolves with the temporal structures, focusing on the growth dynamics of the epidemics. The model assumes no underlying topological structure and is only constrained by the time between two consecutive events of vertex activation. The main observation is that the speed of the infection spread is different in case of heterogeneous and homogeneous temporal patterns but the differences depend on the stage of the epidemics. In comparison to the homogeneous scenario, the power law case results in a faster growth in the beginning but turns out to be slower after a certain time, taking several time steps to reach the whole network."

"Social media comprises interactive applications and platforms for creating, sharing and exchange of user-generated contents. The past ten years have brought huge growth in social media, especially online social networking services, and it is changing our ways to organize and communicate. It aggregates opinions and feelings of diverse groups of people at low cost. Mining the attributes and contents of social media gives us an opportunity to discover social structure characteristics, analyze action patterns qualitatively and quantitatively, and sometimes the ability to predict future human related events. In this paper, we firstly discuss the realms which can be predicted with current social media, then overview available predictors and techniques of prediction, and finally discuss challenges and possible future directions."

"Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes -- in which final state can be obtained by studying the underlying network percolation properties -- have raised formidable interest. In this paper, we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability. As previously demonstrated, the multitype approach allows many non-trivial mixing patterns such as assortativity and clustering between nodes. We derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion. We also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism. We further show that the multitype approach, by naturally allowing heterogeneity in the bond occupation probability, overcomes some of the correlation issues encountered by previous models. We illustrate this point in the context of contact network epidemiology."

"There is great interest in the dynamics of health behaviors in social networks and how they affect collective public health outcomes, but measuring population health behaviors over time and space requires substantial resources. Here, we use publicly available data from 101,853 users of online social media collected over a time period of almost six months to measure the spatio-temporal sentiment towards a new vaccine. We validated our approach by identifying a strong correlation between sentiments expressed online and CDC-estimated vaccination rates by region. Analysis of the network of opinionated users showed that information flows more often between users who share the same sentiments - and less often between users who do not share the same sentiments - than expected by chance alone. We also found that most communities are dominated by either positive or negative sentiments towards the novel vaccine. Simulations of infectious disease transmission show that if clusters of negative vaccine sentiments lead to clusters of unprotected individuals, the likelihood of disease outbreaks is greatly increased. Online social media provide unprecedented access to data allowing for inexpensive and efficient tools to identify target areas for intervention efforts and to evaluate their effectiveness."

"Disease awareness in infection dynamics can be modeled with adaptive contact networks whose rewiring rules reflect the attempt by susceptibles to avoid infectious contacts. Simulations of this type of models show an active phase with constant infected node density in which the interplay of disease dynamics and link rewiring prompts the convergence towards a well defined degree distribution, irrespective of the initial network topology. We develop a method to study this dynamic equilibrium and give an analytic description of the structure of the characteristic degree distributions and other network measures. The method applies to a broad class of systems and can be used to determine the steady-state topology of many other adaptive networks."

"Despite its importance for rumors or innovations propagation, peer-to-peer collaboration, social networking, or marketing, the dynamics of information spreading is not well understood. Since the diffusion depends on the heterogeneous patterns of human behavior and is driven by the participants’ decisions, its propagation dynamics shows surprising properties not explained by traditional epidemic or contagion models. Here we present a detailed analysis of our study of real viral marketing campaigns where tracking the propagation of a controlled message allowed us to analyze the structure and dynamics of a diffusion graph involving over 31 000 individuals. We found that information spreading displays a non-Markovian branching dynamics that can be modeled by a two-step Bellman-Harris branching process that generalizes the static models known in the literature and incorporates the high variability of human behavior. It explains accurately all the features of information propagation under the “tipping point” and can be used for prediction and management of viral information spreading processes."

Even the abstract was tl;dr.

"In this paper we present a new ODE based framework for modelling disease transmission on dynamic contact networks. We adapt and extend the effective degree model for a static network to account for the random creation and deletion of links between individuals. The resulting set of ODEs is solved numerically and results are compared to those obtained using individual-based stochastic network simulations. We show that the ODEs display excellent agreement for the evolution of both the disease and the network, and is able to accurately capture the epidemic threshold for a wide range of parameters. Using the proposed model we show that mild epidemics can be controlled while keeping the contact network well connected, and this is in contrast with severe epidemics, where successful control via link removal leads to a disconnected network."

"Studies of disease spreading on complex networks have provided a deep insight into the conditions of onset, dynamics and prevention of epidemics in human populations and malicious software propagation in computer networks. Identifying nodes which, when initially infected, infect the largest part of the network and ranking them according to their epidemic impact is a priority for public health policies. In simulations of the disease spreading in SIR model on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dynamical dependence is illustrated in an analytically tractable example. A measure called epidemic centrality, averaging the epidemic impact over all possible disease spreading regimes, is introduced as a basis of epidemic ranking. Contrary to standard notion, the epidemic centrality of nodes with high degree, k-cores value or betweenness, which are structurally central, is comparable to epidemic centrality of structurally peripheral nodes. These findings indicate that the impact of an epidemic starting at structurally peripheral nodes may be considerably underestimated. Network periphery should gain a more prominent role in the allocation of resources in future epidemic preparedness plans."

"Recent research has explored the increasingly important role of social media by examining the dynamics of individual and group behavior, characterizing patterns of information diffusion, and identifying influential individuals. In this paper we suggest a measure of causal relationships between nodes based on the information-theoretic notion of transfer entropy, or information transfer. This theoretically grounded measure is based on dynamic information, captures fine-grain notions of influence, and admits a natural, predictive interpretation. Causal networks inferred by transfer entropy can differ significantly from static friendship networks because most friendship links are not useful for predicting future dynamics. We demonstrate through analysis of synthetic and real-world data that transfer entropy reveals meaningful hidden network structures. In addition to altering our notion of who is influential, transfer entropy allows us to differentiate between weak influence over large groups and strong influence over small groups."

"The paper examines the influence of geographic distance, national boundaries, language, and frequency of air travel on the formation of social ties on Twitter, a popular micro-blogging website. Based on a large sample of publicly available Twitter data, our study shows that a substantial share of ties lies within the same metropolitan region, and that between regional clusters, distance, national borders and language differences all predict Twitter ties. We find that the frequency of airline flights between the two parties is the best predictor of Twitter ties. This highlights the importance of looking at pre-existing ties between places and people." --- Not surprising, but I guess good to have confirmed.

There's an arxiv version as well...

"...Twitter's distinction between different types o interactions allows us to establish a parallelism between online and offline social networks: personal interactions are more likely to occur on internal links of groups (the weakness of strong ties), events transmitting information pass preferentially through links connecting different groups or even more through users acting as bridges between groups (the strength of weak ties)."

Good, though not earth-shaking.

"We propose a class of random scale-free spatial networks with nested community structures and analyze Reed-Frost epidemics with community related independent transmissions. We show that the epidemic threshold may be trivial or not depending on the relation among community sizes, distribution of the number of communities and transmission rates"

" These findings underscore the fundamental difference between information spread and other contagion processes: despite multiple opportunities for infection within a social group, people are less likely to become spreaders of information with repeated exposure."

"For a broad range single-seed contagion processes acting on generalized random networks, we derive a unifying analytic expression for the possibility of global spreading events in a straightforward, physically intuitive fashion. Our reasoning lays bare a direct mechanical understanding of an archetypal spreading phenomena that is not evident in circuitous extant mathematical approaches."  (Are they really that circuitous?)

We consider a decision network on an undirected graph in which each node corresponds to a decision variable, and each node and edge of the graph is associated with a reward function whose value depends only on the variables of the corresponding nodes. The goal is to construct a decision vector which maximizes the total reward. This decision problem encompasses a variety of models, including maximum-likelihood inference in graphical models (Markov Random Fields), combinatorial optimization on graphs, economic team theory and statistical physics. The network is endowed with a probabilistic structure in which costs are sampled from a distribution. Our aim is to identify sufficient conditions to guarantee average-case polynomiality of the underlying optimization problem. ... we prove that [in some case we can] find near optimal solutions with high probability in a decentralized way ... based on the network exhibiting a correlation decay (long-range independence) property."

Not sure of the relevance to the "re:" paper. "knowledge acquisition as performed by multiple agents interacting as they infer, under [noise], respective models of a complex system. ... at each time step, each agent takes into account its current observation as well as the average of the models of its neighbors. The agents are connected by a network... of Erdős-Rényi or Barabási-Albert type. .. [if] one [agent] has a different [error rate] (higher or lower). ... [t]he influence of this special agent over the quality of the models inferred by the rest of the network can be substantial, varying linearly with the ... degree of the [special] agent ... [if] the degree of this agent is taken as a respective fitness parameter, the effect of the different [error rate] is ... superlinear.. when the agents are grouped into communities ... edges between agents (within a community) having higher probability of observation error [worsens] the estimation of the agents in the other communities."

"We develop elements of a theory of cooperation and coordination in networks. Rather than considering a communication network as a means of distributing information, or of reconstructing random processes at remote nodes, we ask what dependence can be established among the nodes given the communication constraints. Specifically, in a network with communication rates {R_{i,j}} between the nodes, we ask what is the set of all achievable joint distributions p(x1, ..., xm) of actions at the nodes of the network. Several networks are solved, including arbitrarily large cascade networks.
Distributed cooperation can be the solution to many problems such as distributed games, distributed control, and establishing mutual information bounds on the influence of one part of a physical system on another."

Well, their power law estimation is bad, of course, but more to the point I don't think they're really dealing with an interesting version of the thesis they set out to undermine. (At the very least: even if geography was irrelevant for Internet users, the latter are not uniformly distributed geographically.) The pictures of the diffusion of baby names are cool, though.

"We consider the algorithmic problem of selecting a set of target nodes that cause the biggest activation cascade in a network. In case when the activation process obeys the diminishing return property, a simple hill-climbing selection mechanism has been shown to achieve a provably good performance. Here we study models of influence propagation that exhibit critical behavior and where the property of diminishing returns does not hold. We demonstrate that in such systems the structural properties of networks can play a significant role. We focus on networks with two loosely coupled communities and show that the double-critical behavior of activation spreading in such systems has significant implications for the targeting strategies. In particular, we show that simple strategies that work well for homogenous networks can be overly suboptimal and suggest simple modification for improving the performance by taking into account the community structure."

The null hypothesis, for non-contagious diseases, is IID onset times, i.e., no dependence between onset times for people near each other in the social network. So it doesn't have power against homophily on traits which affect (or even just predict!) the disease.

"We study the spreading of an infection within an SIS epidemiological model on a network. Susceptible agents are given the opportunity of breaking their links with infected agents. Broken links are either permanently removed or reconnected with the rest of the population. Thus, the network coevolves with the population as the infection progresses. We show that a moderate reconnection frequency is enough to completely suppress the infection. A partial, rather weak isolation of infected agents suffices to eliminate the endemic state."