A new betweenness centrality measure based on an algorithm for ranking the nodes of a network

We propose and discuss a new centrality index for urban street patterns represented as networks in geographical space. This centrality measure, that we call ranking-betweenness centrality, combines the idea behind the random-walk betweenness centrality measure and the idea of ranking the nodes of a network produced by an adapted PageRank algorithm. We initially use a PageRank algorithm in which we are able to transform some information of the network that we want to analyze into numerical values. Numerical values summarizing the information are associated to each of the nodes by means of a data matrix. After running the adapted PageRank algorithm, a ranking of the nodes is obtained, according to their importance in the network. This classification is the starting point for applying an algorithm based on the random-walk betweenness centrality. A detailed example of a real urban street network is discussed in order to understand the process to evaluate the ranking-betweenness centrality proposed, performing some comparisons with other classical centrality measures.

Random exams using Sweave

The adaptation of the Spanish University to the European Higher Education Area (EEES in Spanish) demands the integration of new tools and skills that would make the teaching- learning process easier. This adaptation involves a change in the evaluation methods, which goes from a system where the student was evaluated with a final exam, to a new system where we include a continuous evaluation in which the final exam may represent at most 50% in the vast majority of the Universities. Devising a new and fair continuous evaluation system is not an easy task to do. That would mean a student’s’ learning process follow-up by the teachers, and as a consequence an additional workload on existing staff resources. Traditionally, the continuous evaluation is associated with the daily work of the student and a collection of the different marks partly or entirely based on the work they do during the academic year. Now, small groups of students and an attendance control are important aspects to take into account in order to get an adequate assessment of the students. However, most of the university degrees have groups with more than 70 students, and the attendance control is a complicated task to perform, mostly because it consumes significant amounts of staff time. Another problem found is that the attendance control would encourage not-interested students to be present at class, which might cause some troubles to their classmates. After a two year experience in the development of a continuous assessment in Statistics subjects in Social Science degrees, we think that individual and periodical tasks are the best way to assess results. These tasks or examinations must be done in classroom during regular lessons, so we need an efficient system to put together different and personal questions in order to prevent students from cheating. In this paper we provide an efficient and effective way to elaborate random examination papers by using Sweave, a tool that generates data, graphics and statistical calculus from the software R and shows results in PDF documents created by Latex. In this way, we will be able to design an exam template which could be compiled in order to generate as many PDF documents as it is required, and at the same time, solutions are provided to easily correct them.