On the limiting behavior of parameter-dependent network centrality measures

We consider a broad class of walk-based, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various well-known centrality indices, including Katz and subgraph centrality. We show that the parameter can be "tuned" to interpolate between degree and eigenvector centrality, which appear as limiting cases. Our analysis helps explain certain correlations often observed between the rankings obtained using different centrality measures, and provides some guidance for the tuning of parameters. We also highlight the roles played by the spectral gap of the adjacency matrix and by the number of triangles in the network. Our analysis covers both undirected and directed networks, including weighted ones. A brief discussion of PageRank is also given.Comment: First 22 pages are the paper, pages 22-38 are the supplementary material

On Two Web IR Boosting Tools: Clustering and Ranking

This thesis investigates several research problems which arise in modern Web Information Retrieval (WebIR). The Holy Grail of modern WebIR is to find a way to organize and to rank results so that the most ``relevant' come first. The first break-through technique was the exploitation of the link structure of the Web graph in order to rank the result pages, using the well-known Hits and Pagerank algorithms. This link-analysis approaches have been improved and extended, but yet they seem to be insufficient in providing a satisfying search experience. In a number of situations a flat list of search results is not enough, and the users might desire to have search results grouped on-the-fly in folders of similar topics. In addition, the folders should be annotated with meaningful labels for rapid identification of the desired group of results. In other situations, users may have different search goals even when they express them with the same query. In this case the search results should be personalized according to the users' on-line activities. In order to address this need, we will discuss the algorithmic ideas behind SnakeT, a hierarchical clustering meta-search engine which personalizes searches according to the clusters selected by users on-the-fly. There are also situations where users might desire to access fresh information. In these cases, traditional link analysis could not be suitable. In fact, it is possible that there is not enough time to have many links pointing to a recently produced piece of information. In order to address this need, we will discuss the algorithmic and numerical ideas behind a new ranking algorithm suitable for ranking fresh type of information, such as news articles or blogs. When link analysis suffices to produce good quality search results, the huge amount of Web information asks for fast ranking methodologies. We will discuss numerical methodologies for accelerating the eingenvector-like computation, commonly used by link analysis. An important result of this thesis is that we show how to address the above predominant issues of Web Information Retrieval by using clustering and ranking methodologies. We will demonstrate that both clustering and ranking have a mutual reinforcement propriety which has not yet been studied intensively. This propriety can be exploited to boost the precision of both the two methodologies

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

Supplier Ranking System and Its Effect on the Reliability of the Supply Chain

Today, due to the growing use of social media and an increase in the number of A HITS with a solution in PageRank (Massimo, 2011) sharing their opinions globally, customers can review products and services in many novel ways. However, since most reviewers lack in-depth technical knowledge, the true picture concerning product quality remains unclear. Furthermore, although product defects may come from the supplier side, making it responsible for repair cost, it is ultimately the manufacturer whose name is damaged when such defects are revealed. In this context, we need to revisit the cost vs. quality equations. Observations of customer behavior towards brand name and reputation suggest that, contrary to the currently dominant model in production where manufacturers are expected to control only Tier 1 supplier and make it responsible for all higher tiers, manufacturers should also have a better hold on the entire supply chain. Said differently, while the current system considers all parts in Tier 1 as equally important, it underestimates the importance of the impact of each piece on the final product. Another flaw of the current system is that, by commonizing the pieces in several different products, such as different care models of the same manufacturer to reduce the cost, only the supplier of the most common parts will be considered essential and thus get the most attention during quality control. To address the aforementioned concerns, in the present study, we created a parts/supplier ranking algorithm and implemented it into our supply chain system. Upon ranking all suppliers and parts, we calculated the minimum number of the elements, from Tier 1 to Tier 4, that have to be checked in our supply chain. In doing so, we prioritized keeping the cost as low as possible with most inferior possible defects