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

08191 Abstracts Collection -- Graph Drawing with Applications to Bioinformatics and Social Sciences

From May 4 to May 9, 2008, the Dagstuhl Seminar 08191 ``Graph Drawing with Applications to Bioinformatics and Social Sciences\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

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

Brokering Trust to Enhance Leadership: A Self-Monitoring Approach to Leadership Emergence

What kind of person is likely to emerge as an informal leader in the workplace? Experimental research shows that high self-monitors—who tend to adjust their attitudes and behaviors to the demands of different situations—emerge as informal leaders in temporary groups. By contrast, low self-monitors—who tend to be true to themselves in terms of consistency in attitudes and behaviors across different situations—are less likely to emerge as leaders. But this prior research does not address the criticism that the emergence of high self-monitors as leaders represents ephemeral impression management in the context of laboratory experiments. To address this issue, we collected and analyzed data from a 116-member high-technology firm. Our results show that self-monitoring is related not only to leadership emergence, but also to the provision of advice to co-workers. Further, people who occupied brokerage positions (being trusted by those who did not trust each other) tended to be seen as leaders if they were high rather than low self-monitors. From these results, we build a picture of the high self-monitoring emergent leader as someone who notices problems and ameliorates them through the provision of advice and the brokerage of relationships across social divides. The occupation of a structurally advantageous position may well be more advantageous for some (i.e., high self-monitors) relative to others (i.e., low self-monitors)

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