An important invariant of translations of infinite locally finite graphs is that of a direction as introduced by HALIN. This invariant gives not much information if the translation is not a proper one. A new refined concept of directions is investigated.A double ray D of a graph X is said to be metric, if the distance metrics in D and X on V ( D ) are equivalent. It is called geodesic, if these metrics are equal. The translations leaving some metric double ray invariant are characterized. Using a result of POLAT and WATKINS, we characterize the translations leaving some geodesic double ray invariant.
Most network studies rely on a measured network that differs from the underlying network which is obfuscated by measurement errors. It is well known that such errors can have a severe impact on the reliability of network metrics, especially on centrality measures: a more central node in the observed network might be less central in the underlying network. Previous studies have dealt either with the general effects of measurement errors on centrality measures or with the treatment of erroneous network data. In this paper, we propose a method for estimating the impact of measurement errors on the reliability of a centrality measure, given the measured network and assumptions about the type and intensity of the measurement error. This method allows researchers to estimate the robustness of a centrality measure in a specific network and can, therefore, be used as a basis for decision-making. In our experiments, we apply this method to random graphs and real-world networks. We observe that our estimation is, in the vast majority of cases, a good approximation for the robustness of centrality measures. Beyond this, we propose a heuristic to decide whether the estimation procedure should be used. We analyze, for certain networks, why the eigenvector centrality is less robust than, among others, the pagerank. Finally, we give recommendations on how our findings can be applied to future network studies.
Big Data is one of the latest emerging topics in the field of business information systems, and is marketed as being the key for companies future success. Many analytic solutions are offered by IT companies to help other businesses with the flood of data that is generated within and outside of a company. Despite the extensive use of the notion Big Data for marketing purposes, there is no common understanding of how to characterize the elements of the Big Data concept. The authors contribute to the clarification of this concept with a methodologically enriched literature review by deriving characteristic dimensions from existing definitions of Big Data. These dimensions are validated and enriched with a two-step approach by applying topic models on 248 publications relevant to Big Data. The authors propose that the concept of Big Data can be described by the dimensions of data, IT infrastructure, applied methods, and an applications perspective. The assignment of the results to a generic data analysis process reveals that recent publications focus on data analysis and processing, and less attention is given to the initial data selection or the visualization and utilization of the analysis results.
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