Estudio experimental del Forward Linear Threshold Rank

La centralidad y la difusión de influencia son dos de los conceptos más estudiados en el análisis de redes sociales. La mayoría de medidas de centralidad propuestas, se basan en características topológicas de la red. Recientemente se han propuesto nuevas medidas de centralidad basadas en los dos principales modelos de difusión de influencia, el Independent Cascade Model y el Linear Threshold Model. Una de estas medidas basadas en estos modelos es el Linear Threshold Rank, la cual se define como el numero de nodos influenciados cuando el conjunto de activación inicial es formado por el mismo nodo y sus vecinos inmediatos. En este proyecto, introducimos nuevas medidas de centralidad basadas en esta medida y continuaremos con el análisis de otras medidas basadas en este mismo modelo y en otras variantes de él. Compararemos estas medidas con otras ya conocidas, utilizando diferentes herramientas para el análisis de desigualdad en redes. Propondremos un algoritmo simple y eficiente, para calcularlas, y lo implementaremos en C++ para reducir los tiempos de ejecución. Finalmente, publicaremos los resultados en una plataforma online, para que puedan ser consultados y contrastados fácilmente.Centrality and spread of influence are two of the most studied concepts in the analysis of social networks. Most of the proposed centrality measures are based on topological characteristics of the network. Recently new centrality measures have been proposed inspired by the two main influence spread models, the Independent Cascade Model and the Linear Threshold Model. One of these measures based on these models is the Linear Threshold Rank, which is defined as the number of influenced nodes when the initial activation set is formed by the node itself and its immediate neighbours. In this project, we introduce new centrality measures based on this measure and we will continue with the analysis of other measures based on this same model and other variants of it. We will compare these measures with others already known, using different tools for the analysis of inequality in networks. We will propose a simple and efficient algorithm, to calculate them, and we will implement it in C++ to reduce the execution times. Finally, we will publish the results in an online platform, in order to be easily consulted and contrasted

Non-Conservative Diffusion and its Application to Social Network Analysis

The random walk is fundamental to modeling dynamic processes on networks. Metrics based on the random walk have been used in many applications from image processing to Web page ranking. However, how appropriate are random walks to modeling and analyzing social networks? We argue that unlike a random walk, which conserves the quantity diffusing on a network, many interesting social phenomena, such as the spread of information or disease on a social network, are fundamentally non-conservative. When an individual infects her neighbor with a virus, the total amount of infection increases. We classify diffusion processes as conservative and non-conservative and show how these differences impact the choice of metrics used for network analysis, as well as our understanding of network structure and behavior. We show that Alpha-Centrality, which mathematically describes non-conservative diffusion, leads to new insights into the behavior of spreading processes on networks. We give a scalable approximate algorithm for computing the Alpha-Centrality in a massive graph. We validate our approach on real-world online social networks of Digg. We show that a non-conservative metric, such as Alpha-Centrality, produces better agreement with empirical measure of influence than conservative metrics, such as PageRank. We hope that our investigation will inspire further exploration into the realms of conservative and non-conservative metrics in social network analysis

Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods

Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.Comment: 24 pages, 10 figure

A measure of individual role in collective dynamics

Identifying key players in collective dynamics remains a challenge in several research fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. The difficulty lies at several levels: how to single out the role of individual elements in such intermingled systems, or which is the best way to quantify their importance. Centrality measures describe a node's importance by its position in a network. The key issue obviated is that the contribution of a node to the collective behavior is not uniquely determined by the structure of the system but it is a result of the interplay between dynamics and network structure. We show that dynamical influence measures explicitly how strongly a node's dynamical state affects collective behavior. For critical spreading, dynamical influence targets nodes according to their spreading capabilities. For diffusive processes it quantifies how efficiently real systems may be controlled by manipulating a single node.Comment: accepted for publication in Scientific Report