Covert networks are social networks that often consist of harmful users. Social Network Analysis (SNA) has played an important role in reducing criminal activities (e.g., counter terrorism) via detecting the influential users in such networks. There are various popular measures to quantify how influential or central any vertex is in a network. As expected, strategic and influential miscreants in covert networks would try to hide herself and her partners (called leaders ) from being detected via these measures by introducing new edges. show that the corresponding computational problem, called Hiding Leader, is NP-Complete for the degree and closeness centrality measures. We study the popular core centrality measure and show that the problem is NP-Complete even when the core centrality of every leader is only @math . On the contrary, we prove that the problem becomes polynomial time solvable for the degree centrality measure if the degree of every leader is bounded above by any constant. We then focus on the optimization version of the problem and show that the Hiding Leader problem admits a @math factor approximation algorithm for the degree centrality measure. We complement it by proving that one cannot hope to have any @math factor approximation algorithm for any constant @math unless there is a @math factor polynomial time algorithm for the Densest @math -Subgraph problem which would be considered a significant breakthrough.
Reduction of end-to-end network delay is an optimization task with applications in multiple domains. Low delays enable improved information flow in social networks, quick spread of ideas in collaboration networks, low travel times for vehicles on road networks, and increased rate of packets in the case of communication networks. Delay reduction can be achieved by both improving the propagation capabilities of individual nodes and adding additional edges in the network. One of the main challenges in such network design problems is that the effects of local changes are not independent, and as a consequence, there is a combinatorial search-space of possible improvements. Thus, minimizing the cumulative propagation delay requires novel scalable and data-driven approaches. We consider the problem of network delay minimization via node upgrades. We show that the problem is NP-hard and prove strong inapproximability results about it (i.e., APX-hard) even for equal vertex delays. On the positive side, probabilistic approximations for a restricted version of the problem can be obtained. We propose a greedy heuristic to solve the general problem setting which has good quality in practice, but does not scale to very large instances. To enable scalability to real-world networks, we develop approximations for Greedy with probabilistic guarantees for every iteration, tailored to different models of delay distribution and network structures. Our methods scale almost linearly with the graph size and consistently outperform competitors in quality. We evaluate our approaches on several real-world graphs from different genres. We achieve up to two orders of magnitude speed-up compared to alternatives from the literature on moderate size networks, and obtain high-quality results in minutes on large datasets while competitors from the literature require more than four hours.    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.  Graphs with weights and delays associated with their edges and or vertices are often used to model communication and signal flow networks. Network performance can be improved by upgrading the network vertices. Such an upgrade reduces the edge vertex delays and comes at a cost. We study different formulations of this network performance improvement problem and show that these are NP-hard. We then consider one of the formulations and develop polynomial time algorithms for some special cases and pseudopolynomial time algorithms for others. Elections involving a large voter population often lead to outcomes that surprise many. A better prediction of the true outcome helps reduce the adverse effect of surprise on the economy of a sizable population. This paper starts from the basic observation that individuals in the underlying population build estimates of the distribution of preferences of the whole population based on their immediate neighbors in the underlying social network. The outcome of the election leads to a surprise if these local estimates contradict the outcome of the election for some fixed voting rule. To get a quantitative understanding, we propose a novel mathematical model of the setting where the individuals in the population and their connections are described by a random graph with connection probabilities that are biased based on the preferences of the individuals. Each individual also has some estimate of the bias in their connections. The connection model is inspired by the homophily effect in social networks. We show that the election outcome leads to a surprise if the discrepancy between the estimated bias and the true bias in the local connections exceeds a certain threshold, and confirm the phenomenon that surprising outcomes are associated only with closely contested elections. We consider large elections with networked voters and compare standard voting rules based on their performance on surprise. Our results show that the rules have different behavior for different parts of the population. It also hints at an impossibility result that any reasonable voting rule will be less surprising for all parts of a population. To attest some of our theoretical predictions, we experiment with the large dataset of UK-EU referendum (a.k.a. Brexit).  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.