Ranking in evolving complex networks

Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world problems because it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and policymakers, among others. This calls for a deep understanding of how existing ranking algorithms perform, and which are their possible biases that may impair their effectiveness. Many popular ranking algorithms (such as Google’s PageRank) are static in nature and, as a consequence, they exhibit important shortcomings when applied to real networks that rapidly evolve in time. At the same time, recent advances in the understanding and modeling of evolving networks have enabled the development of a wide and diverse range of ranking algorithms that take the temporal dimension into account. The aim of this review is to survey the existing ranking algorithms, both static and time-aware, and their applications to evolving networks. We emphasize both the impact of network evolution on well-established static algorithms and the benefits from including the temporal dimension for tasks such as prediction of network traffic, prediction of future links, and identification of significant nodes

Whittle Index Policy for Crawling Ephemeral Content

We consider the task of scheduling a crawler to retrieve from several sites their ephemeral content. This is content, such as news or posts at social network groups, for which a user typically loses interest after some days or hours. Thus, the development of a timely crawling policy for ephemeral information sources is very important. We first formulate this problem as an optimal control problem with average reward. The reward can be measured in terms of the number of clicks or relevant search requests. The problem in its exact formulation suffers from the curse of dimensionality and quickly becomes intractable even with a moderate number of information sources. Fortunately, this problem admits a Whittle index, a celebrated heuristics which leads to problem decomposition and to a very simple and efficient crawling policy. We derive the Whittle index for a simple deterministic model and provide its theoretical justification. We also outline an extension to a fully stochastic model

Perturbation analysis for denumerable Markov chains with application to queueing models

We study the parametric perturbation of Markov chains with denumerable state space. We consider both regular and singular perturbations. By the latter we mean that transition probabilities of a Markov chain, which has several ergodic classes, is perturbed in a way that allows rare transitions between the different ergodic classes of the unperturbed chain. In the previous works the singularly perturbed Markov chains were studied under restrictive assumptions such as strong recurrence ergodicity or Doeblin conditions. Our goal is to relax these by conditions that can be applied to queueing models (where the conditions mentioned above typically fail to hold). With the help of the $\nu$-geometric ergodicity approach, we are able to express explicitly the steady state distribution of the perturbed Markov chain as a Taylor series in the perturbation parameter. We apply our tools to quasi birth and death processes and provide queueing examples

Almost Exact Recovery in Label Spreading

International audienceIn semi-supervised graph clustering setting, an expert provides cluster membership of few nodes. This little amount of information allows one to achieve high accuracy clustering using efficient computational procedures. Our main goal is to provide a theoretical justification why the graph-based semi-supervised learning works very well. Specifically, for the Stochastic Block Model in the moderately sparse regime, we prove that popular semi-supervised clustering methods like Label Spreading achieve asymptotically almost exact recovery as long as the fraction of labeled nodes does not go to zero and the average degree goes to infinity