El problema del actor clave

Se describe un procedimiento para identificar actores clave en una red social. Un supuesto básico es que la selección optima depende de los fines de dicha selección. De acuerdo con ello, se articulan dos metas genéricas, referidas al problema del actor clave en términos positivos y negativos. Primero se propone un procedimiento para identificar actores clave con el objetivo de difundir algo de manera óptima en la red, valiéndose de los actores clave como semillas. El segundo procedimiento identifica actores clave con el objetivo de perturbar o fragmentar la red eliminando algunos de sus nodos. Los indicadores de centralidad habituales no son óptimos para este propósito, por lo que se proponen nuevos indicadores.A procedure is described for finding sets of key players in a social network. A key assumption is that the optimal selection of key players depends on what they are needed for. Accordingly, two generic goals are articulated, referring to key player problem in positive (KPP-1) and negative (KPP-2) terms. KPP-1 is defined as the identification of key players for the purpose of optimally diffusing something through the network by using the key players as seeds. KPP-2 is defined as the identification of key players for the purpose of disrupting or fragmenting the network by removing the key nodes. It is found that off-the-shelf centrality measures are not optimal for solving either generic problem, and therefore new measures are presented

Techniques: Dichotomizing a Network

This techniques guide provides a brief answer to the question: How to choose a dichotomization threshold? We propose a two step approach to selecting a dichotomization threshold. We illustrate the approaches using two datasets and provide instructions on how to perform these approaches in R and UCINET

Centrality in valued graphs: A measure of betweenness based on network flow

A new measure of centrality, C,, is introduced. It is based on the concept of network flows. While conceptually similar to Freeman’s original measure, Ca, the new measure differs from the original in two important ways. First, C, is defined for both valued and non-valued graphs. This makes C, applicable to a wider variety of network datasets. Second, the computation of C, is not based on geodesic paths as is C, but on all the independent paths between all pairs of points in the network

Percolation theory applied to measures of fragmentation in social networks

We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction $q$ of nodes and the total number of pairs in the original fully connected network. We compare $F$ with the traditional measure used in percolation theory, $P_{\infty}$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods from percolation, we study Erd\H{o}s-R\'{e}nyi (ER) and scale-free (SF) networks under various types of node removal strategies. The removal strategies are: random removal, high degree removal and high betweenness centrality removal. We find that for a network obtained after removal (all strategies) of a fraction $q$ of nodes above percolation threshold, $P_{\infty}\approx (1-F)^{1/2}$. For fixed $P_{\infty}$ and close to percolation threshold ($q=q_c$), we show that $1-F$ better reflects the actual fragmentation. Close to $q_c$, for a given $P_{\infty}$, $1-F$ has a broad distribution and it is thus possible to improve the fragmentation of the network. We also study and compare the fragmentation measure $F$ and the percolation measure $P_{\infty}$ for a real social network of workplaces linked by the households of the employees and find similar results.Comment: submitted to PR

Imaginary Worlds: Using Visual Network Scales to Capture Perceptions of Social Networks

Social networks are not just patterns of interaction and sentiment in the real world; they are also cognitive (re)constructions of social relations, some real, some imagined. Focusing on networks as mental entities, our essay describes a new method that relies on stylized network images to gather quantitative data on how people “see” specific aspects of their social worlds. We discuss the logic of our approach, present several examples of “visual network scales,” discuss some preliminary findings, and identify some of the problems and prospects in this nascent line of work on the phenomenology of social networks