Society is often polarized by controversial issues, that split the population into groups of opposing views. When such issues emerge on social media, we often observe the creation of 'echo chambers', i.e., situations where like-minded people reinforce each other's opinion, but do not get exposed to the views of the opposing side. In this paper we study algorithmic techniques for bridging these chambers, and thus, reducing controversy. Specifically, we represent the discussion on a controversial issue with an endorsement graph, and cast our problem as an edge-recommendation problem on this graph. The goal of the recommendation is to reduce the controversy score of the graph, which is measured by a recently-developed metric based on random walks. At the same time, we take into account the acceptance probability of the recommended edge, which represents how likely the edge is to materialize in the endorsement graph. We propose a simple model based on a recently-developed user-level controversy score, that is competitive with state-of- the-art link-prediction algorithms. We thus aim at finding the edges that produce the largest reduction in the controversy score, in expectation. To solve this problem, we propose an efficient algorithm, which considers only a fraction of all the combinations of possible edges. Experimental results show that our algorithm is more efficient than a simple greedy heuristic, while producing comparable score reduction. Finally, a comparison with other state-of-the-art edge-addition algorithms shows that this problem is fundamentally different from what has been studied in the literature.
The paper that is is conceptually closest to ours is the one by @cite_34 , which aims to add and remove edges in a graph to reduce the dissemination of content (e.g., viruses). The proposed approach is to try to maximize the largest eigenvalue, which determines the epidemic threshold and, thus, the properties of information dissemination in networks.
@cite_34
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Controlling the dissemination of an entity (e.g., meme, virus, etc) on a large graph is an interesting problem in many disciplines. Examples include epidemiology, computer security, marketing, etc. So far, previous studies have mostly focused on removing or inoculating nodes to achieve the desired outcome. We shift the problem to the level of edges and ask: which edges should we add or delete in order to speed-up or contain a dissemination? First, we propose effective and scalable algorithms to solve these dissemination problems. Second, we conduct a theoretical study of the two problems and our methods, including the hardness of the problem, the accuracy and complexity of our methods, and the equivalence between the different strategies and problems. Third and lastly, we conduct experiments on real topologies of varying sizes to demonstrate the effectiveness and scalability of our approaches. Given a network of who-contacts-whom or who-links-to-whom, will a contagious virus product meme spread and ‘take over’ (cause an epidemic) or die out quickly? What will change if nodes have partial, temporary or permanent immunity? The epidemic threshold is the minimum level of virulence to prevent a viral contagion from dying out quickly and determining it is a fundamental question in epidemiology and related areas. Most earlier work focuses either on special types of graphs or on specific epidemiological cascade models. We are the first to show the G2-threshold (twice generalized) theorem, which nicely de-couples the effect of the topology and the virus model. Our result unifies and includes as special case older results and shows that the threshold depends on the first eigenvalue of the connectivity matrix, (a) for any graph and (b) for all propagation models in standard literature (more than 25, including H.I.V.). Our discovery has broad implications for the vulnerability of real, complex networks and numerous applications, including viral marketing, blog dynamics, influence propagation, easy answers to ‘what-if’ questions, and simplified design and evaluation of immunization policies. We also demonstrate our result using extensive simulations on real networks, including on one of the biggest available social-contact graphs containing more than 31 million interactions among more than 1 million people representing the city of Portland, Oregon, USA. This paper studies the problem of detecting the information source in a network in which the spread of information follows the popular Susceptible-Infected-Recovered (SIR) model. We assume all nodes in the network are in the susceptible state initially except the information source which is in the infected state. Susceptible nodes may then be infected by infected nodes, and infected nodes may recover and will not be infected again after recovery. Given a snapshot of the network, from which we know all infected nodes but cannot distinguish susceptible nodes and recovered nodes, the problem is to find the information source based on the snapshot and the network topology. We develop a sample path based approach where the estimator of the information source is chosen to be the root node associated with the sample path that most likely leads to the observed snapshot. We prove for infinite-trees, the estimator is a node that minimizes the maximum distance to the infected nodes. A reverse-infection algorithm is proposed to find such an estimator in general graphs. We prove that for g-regular trees such that gq > 1, where g is the node degree and q is the infection probability, the estimator is within a constant distance from the actual source with high probability, independent of the number of infected nodes and the time the snapshot is taken. Our simulation results show that for tree networks, the estimator produced by the reverse-infection algorithm is closer to the actual source than the one identified by the closeness centrality heuristic. In this paper, we consider the problem of locating the information source with sparse observations. We assume that a piece of information spreads in a network following a heterogeneous susceptible-infected-recovered (SIR) model and that a small subset of infected nodes are reported, from which we need to find the source of the information. We adopt the sample path based estimator developed in [1], and prove that on infinite trees, the sample path based estimator is a Jordan infection center with respect to the set of observed infected nodes. In other words, the sample path based estimator minimizes the maximum distance to observed infected nodes. We further prove that the distance between the estimator and the actual source is upper bounded by a constant independent of the number of infected nodes with a high probability on infinite trees. Our simulations on tree networks and real world networks show that the sample path based estimator is closer to the actual source than several other algorithms.