Modelling information cascades over online social networks is important in fields from marketing to civil unrest prediction, however the underlying network structure strongly affects the probability and nature of such cascades. Even with simple cascade dynamics the probability of large cascades are almost entirely dictated by network properties, with well-known networks such as Erdos-Renyi and Barabasi-Albert producing wildly different cascades from the same model. Indeed, the notion of 'superspreaders' has arisen to describe highly influential nodes promoting global cascades in a social network. Here we use a simple model of global cascades to show that the presence of locality in the network increases the probability of a global cascade due to the increased vulnerability of connecting nodes. Rather than 'super-spreaders', we find that the presence of these highly connected 'super-blockers' in heavy-tailed networks in fact reduces the probability of global cascades, while promoting information spread when targeted as the initial spreader.

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Contagion processes are strongly linked to the network structures on which they propagate, and learning these structures is essential for understanding and intervention on complex network processes such as epidemics and (mis)information propagation. However, using contagion data to infer network structure is a challenging inverse problem. In particular, it is imperative to have appropriate measures of uncertainty in network structure estimates, however these are largely ignored in most machine-learning approaches. We present a probabilistic framework that uses samples from the distribution of networks that are compatible with the dynamics observed to produce network and uncertainty estimates. We demonstrate the method using the well known independent cascade model to sample from the distribution of networks P(G) conditioned on the observation of a set of infections C. We evaluate the accuracy of the method by using the marginal probabilities of each edge in the distribution, and show the benefits of quantifying uncertainty to improve estimates and understanding, particularly with small amounts of data.

Sampling random graphs is essential in many applications, and often algorithms use Markov chain Monte Carlo methods to sample uniformly from the space of graphs. However, often there is a need to sample graphs with some property that we are unable, or it is too inefficient, to sample using standard approaches. In this paper we are interested in sampling graphs from a conditional ensemble of the underlying graph model. We present an algorithm to generate samples from an ensemble of connected random graphs using a Metropolis-Hastings framework. The algorithm extends to a general framework for sampling from a known distribution of graphs, conditioned on a desired property. We demonstrate the method to generate connected spatially embedded random graphs, specifically the well known Waxman network, and illustrate the convergence and practicalities of the algorithm.