Jose F. Vicent

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

Abstract 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.

A Non-abelian Group Based on Block Upper Triangular Matrices with Cryptographic Applications

The aim of this article is twofold. In the first place, we describe a special non-abelian group of block upper triangular matrices, and verify that choosing properly certain parameters, the order of the subgroup generated by one of these matrices can be as large as needed. Secondly, we propose and implement a new key exchange scheme based on these primitives. The security of the proposed system is based on discrete logarithm problem although a non-abelian group of matrices is used. The primary advantadge of this scheme is that no prime numbers are used and the efficiency is guaranteed by the use of a quick exponentiation algorithm for this group of matrices.

Different Types of Graphs to Model a City

This work was partially supported by the Spanish Government, Ministerio de Economia y Competividad, which reference number is TIN2014-53855-P.

A centrality measure for urban networks based on the eigenvector centrality concept

A massive amount of information as geo-referenced data is now emerging from the digitization of contemporary cities. Urban streets networks are characterized by a fairly uniform degree distribution and a low degree range. Therefore, the analysis of the graph constructed from the topology of the urban layout does not provide significant information when studying topology-based centrality. On the other hand, we have collected geo-located data about the use of various buildings and facilities within the city. This does provide a rich source of information about the importance of various areas. Despite this, we still need to consider the influence of topology, as this determines the interaction between different areas. In this paper, we propose a new model of centrality for urban networks based on the concept of Eigenvector Centrality for urban street networks which incorporates information from both topology and data residing on the nodes. So, the centrality proposed is able to measure the influence of two factors, the topology of the network and the geo-referenced data extracted from the network and associated to the nodes. We detail how to compute the centrality measure and provide the rational behind it. Some numerical examples with small networks are performed to analyse the characteristics of the model. Finally, a detailed example of a real urban street network is discussed, taking a real set of data obtained from a fieldwork, regarding the commercial activity developed in the city.

Analyzing Urban Extensions and Its Effects over the Commercial Activity of an Urban Network

In this paper, we present a way for analyzing and visualizing extensions or enhancements of an existing urban network, as well as the effects that cause these extensions on commercial activity taking place in the network itself. This analysis is based on an algorithm for classifying the nodes of the network, depending on the type and number of facilities allocated to each node. Using this classification, it is possible to visualize the network according to a gradient color scale, allowing us to identify the most important nodes in the network and the part of the network more influenced by the introduction of new facilities. With this classification algorithm we can simulate and evaluate the effect that produces any reform plan over an existing urban street network.

A quick exponentiation algorithm for 3×3 block upper triangular matrices

Abstract Block upper triangular matrices with elements in Z p have very interesting properties for many applications. Some of them involve powers of this type of matrices with very large exponents requiring specific exponentiation algorithms to compute them efficiently. In this paper, we analyze quick exponentiation in block upper triangular matrices of size 3 × 3 blocks as an extension of the quick exponentiation in block upper triangular matrices of 2 × 2 blocks.