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.
Adding edges to modify the graph structure. In addition to the work on explicitly reducing polarization in social media, there are many papers aiming to make a network more cohesive by edge additions, where cohesiveness is quantified using graph-theoretic properties, such as shortest paths @cite_3 @cite_32 , closeness centrality @cite_7 , diameter @cite_0 , eccentricity @cite_11 , communicability @cite_20 @cite_25 , synchronizability @cite_35 , and natural connectivity @cite_17 .
@cite_35 @cite_7 @cite_32 @cite_3 @cite_17 @cite_0 @cite_25 @cite_20 @cite_11
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In this paper, we studied the strategies to enhance synchronization on directed networks by manipulating a fixed number of links. We proposed a centrality-based manipulating (CBM) method, where the node centrality is measured by the well-known PageRank algorithm. Extensive numerical simulation on many modeled networks demonstrated that the CBM method is more effective in facilitating synchronization than the degree-based manipulating method and the random manipulating method for adding or removing links. The reason is that the CBM method can effectively narrow the incoming degree distribution and reinforce the hierarchical structure of the network. Furthermore, we apply the CBM method to the links rewiring procedure where at each step one link is removed and one new link is added. The CBM method helps to decide which links should be removed or added. After several steps, the resulting networks are very close to the optimal structure from the theoretical analysis and the evolutionary optimization algorithm. The numerical simulations on the Kuramoto model further demonstrate that our method has an advantage in shortening the convergence time to synchronization on directed networks. Small changes in the network topology can have dramatic effects on its capacity to disseminate information. In this paper, we consider the problem of adding a small number of ghost edges in the network in order to minimize the average shortest-path distance between nodes, towards a smaller-world network. We formalize the problem of suggesting ghost edges and we propose a novel method for quickly evaluating the importance of ghost edges in sparse graphs. Through experiments on real and synthetic data sets, we demonstrate that our approach performs very well, for a varying range of conditions, and it outperforms sensible baselines. The small world phenomenon is a desirable property of social networks, since it guarantees short paths between the nodes of the social graph and thus efficient information spread on the network. It is thus in the benefit of both network users and network owners to enforce and maintain this property. In this work, we study the problem of finding a subset of k edges from a set of candidate edges whose addition to a network leads to the greatest reduction in its average shortest path length. We formulate the problem as a combinatorial optimization problem, and show that it is NP-hard and that known approximation techniques are not applicable. We describe an efficient method for computing the exact effect of a single edge insertion on the average shortest path length, as well as several heuristics for efficiently estimating this effect. We perform experiments on real data to study the performance of our algorithms in practice. The function and performance of networks rely on their robustness, defined as their ability to continue functioning in the face of damage (targeted attacks or random failures) to parts of the network. Prior research has proposed a variety of measures to quantify robustness and various manipulation strategies to alter it. In this paper, our contributions are twofold. First, we critically analyze various robustness measures and identify their strengths and weaknesses. Our analysis suggests natural connectivity, based on the weighted count of loops in a network, to be a reliable measure. Second, we propose the first principled manipulation algorithms that directly optimize this robustness measure, which lead to significant performance improvement over existing, ad-hoc heuristic solutions. Extensive experiments on real-world datasets demonstrate the effectiveness and scalability of our methods against a long list of competitor strategies. We study the problem of minimizing the diameter of a graph by adding k shortcut edges, for speeding up communication in an existing network design. We develop constant-factor approximation algorithms for different variations of this problem. We also show how to improve the approximation ratios using resource augmentation to allow more than k shortcut edges. We observe a close relation between the single-source version of the problem, where we want to minimize the largest distance from a given source vertex, and the well-known k-median problem. First we show that our constant-factor approximation algorithms for the general case solve the single-source problem within a constant factor. Then, using a linear-programming formulation for the single-source version, we find a (1+e)-approximation using O(klogn) shortcut edges. To show the tightness of our result, we prove that any @math -approximation for the single-source version must use Ω(klogn) shortcut edges assuming P≠NP. The total communicability of a network (or graph) is defined as the sum of the entries in the exponential of the adjacency matrix of the network, possibly normalized by the number of nodes. This quantity offers a good measure of how easily information spreads across the network, and can be useful in the design of networks having certain desirable properties. The total communicability can be computed quickly even for large networks using techniques based on the Lanczos algorithm. In this work we introduce some heuristics that can be used to add, delete, or rewire a limited number of edges in a given sparse network so that the modified network has a large total communicability. To this end, we introduce new edge centrality measures, which can be used as a guide in the selection of edges to be added or removed. Moreover, we show experimentally that the total communicability provides an effective and easily computable measure of how "well-connected" a sparse network is. We introduce new broadcast and receive communicability indices that can be used as global measures of how effectively information is spread in a directed network. Furthermore, we describe fast and effective criteria for the selection of edges to be added to (or deleted from) a given directed network so as to enhance these network communicability measures. Numerical experiments illustrate the effectiveness of the proposed techniques. In practical military or first responder deployment scenarios, information flows need to adhere to specified policies regardless of the physical connectivity of nodes. Nodes in such networks are associated with various levels in a command-and-control hierarchy, and therefore typically form a logical hierarchical tree network that is used to route both command and data traffic. Associated with this logical hierarchical network is a communication network that represents the connectivity of these nodes in the deployed scenario. Such composite networks introduce constraints that can result in information flows having to traverse much longer paths in the underlying communication network. In this paper, we look at the problem of adding edges to a logical hierarchical network (or any other social network) so as to minimize the number of hops required to route data traffic in the underlying communication network from a node to other specified nodes. The edges added are a subset of all possible edges in the complementary logical hierarchical graph and have to satisfy specified hierarchical constraints. First, we consider the general problem of minimizing the eccentricity of a source node 's' (where eccentricity of 's' is the maximum of the shortest paths from 's' to all other nodes) in a metric graph on adding upto 'B' unequal cost metric edges from the set of all edges in the complementary graph. We develop an efficient constant factor approximation algorithm for this case that outperforms existing constant factor algorithms for eccentricity minimization. Here the added edge metric cost as well as the graph edge metric cost correspond to the number of hops in the shortest path required to route traffic in the actual deployed topology (i.e., underlying communication network). Next, we consider the case where the set of possible added edges is a specified subset of the edges in the complementary graph and the set of destinations is a subset of the graph nodes. For this case, we develop heuristic algorithms based on the previous eccentricity minimizing algorithm that show good performance. We validate our algorithms using two realistic military deployment scenarios. We find that adding even a low number of hierarchically constrained edges (of the order of 10) can cause a significant decrease (around 50 ) in the eccentricity of a node in the logical hierarchical network and thus can reduce the number of hops required for data traffic traversal.