SNA provides a wide range of tools that allow examination of telecommunications graphs. Those graphs contain vertices representing cell phone users and lines standing for established connections. Many sna tools do not incorporate the intensity of interaction. This may lead to wrong conclusions because the difference between best friends and random contacts can be defined by the accumulated duration of talks. To solve this problem, we propose a closeness centrality measure (ewc) that incorporates line values and compare it to Freeman's closeness. Small exemplary networks will demonstrate the characteristics of the weighted closeness compared to other centrality measures. Finally, the ewc will be tested on a real-world telecommunications graph provided by a large Austrian mobile service provider and the advantages of the ewc will be discussed. / Series: Research Report Series / Department of Statistics and Mathematics

In Social Network Analysis (SNA) centrality measures focus on activity (degree), information access (betweenness), distance to all the nodes (closeness), or popularity (pagerank). We introduce a new measure quantifying the distance of nodes to the network center. It is called weighted distance to nearest center (WDNC) and it is based on edge-weighted closeness (EWC), a weighted version of closeness. It combines elements of weighted centrality as well as clustering. The WDNC will be tested on two e-mail networks of the R community, one of the most important open source programs for statistical computing and graphics. We will find that there is a relationship between the WDNC and the formal organization of the R community. / Series: Research Report Series / Department of Statistics and Mathematics

The number of systems that collect vast amount of data about users rapidly grow during last few years. Many of these systems contain data not only about people characteristics but also about their relationships with other system users. From this kind of data it is possible to extract a social network that reflects the connections between system’s users. Moreover, the analysis of such social network enables to investigate different characteristics of its users and their linkages. One of the types of examining such network is key users extraction. Key users are these who have the biggest impact on other network users as well as have big influence on network evolution. The obtained knowledge about these users enables to investigate and predict changes within the network. So this knowledge is very important for the people or companies who make a profit from the network like telecommunication company. The second important issue is the ability to extract these users as quick as possible, i.e. developed the algorithm that will be time-effective in large social networks where number of nodes and edges is equal few millions.

Submitted by Silvana Teresinha Dornelles Studzinski (sstudzinski) on 2016-11-17T10:55:05Z No. of bitstreams: 1 Eduardo Nunes dos Reis__.pdf: 3241209 bytes, checksum: b350ca7207662ffbe86ca0164cf92887 (MD5) / Made available in DSpace on 2016-11-17T10:55:06Z (GMT). No. of bitstreams: 1 Eduardo Nunes dos Reis__.pdf: 3241209 bytes, checksum: b350ca7207662ffbe86ca0164cf92887 (MD5) Previous issue date: 2016-01-18 / Nenhuma / Análise de Contingências em sistemas elétricos de transmissão são de fundamental importância tanto para o planejamento quanto para a operação do sistema. Conhecimento do nível de importância e o impacto de interrupções em condições de operação da rede, em cada linha e em todas as barras de carga é crucial para a análise de segurança da rede. Este trabalho tem como objetivo avaliar a fragilidade dos sistemas elétricos de transmissão através de cálculo e análise das centralidades das redes, identificando seus nós mais importantes. Desta forma, pode-se obter informações sobre a rede com um menor custo computacional que as ferramentas disponíveis no momento. Os testes foram aplicados em redes IEEE padrão e em redes reais de grande escala, como o Sistema Interligado Nacional brasileiro (SIN). Os resultados foram comparados com os obtidos no software ANAREDE, software este que possui maior penetração entre as empresas de transmissão, e é baseado em cálculo de fluxo de potência. Com essa comparação é possível avaliar o grau de confiabilidade do método proposto.Os dados analisados mostram que o método pode ser utilizado como uma ferramenta auxiliar de baixo custo computacional para a avaliação de contingências fornecendo subsídios para análises mais aprofundadas dos nós indicados como críticos. Através da utilização do coeficiente de Correlação de Spearman verifica-se que os resultados do cálculo de centralidades possuem boa proximidade aos resultados do ANAREDE, com menor custo computacional e possibilidade de rodarredes de grande densidade de forma completa. / Contingency analysis of an electricity transmission system is of fundamental importance for both planning and system operation. Knowledge of the level of importance and the impact of outage in operating conditions of the network, were each one of the lines and on every load baseline is crucial for the analysis of network security. This work aims to evaluate the fragility of the electricity transmission system through centrality analysis of networks, identifying the most important nodes in the network. On this way, important information of the network can be achieved with lower computation cost than current available tools.Tests were performed on standard IEEE and in actual large scale networks, as the Brazilian National Interconnected Power System (NIPS). The results were compared with optimal results obtained from ANAREDE software, which is based on power flow calculation to check if the centrality-based method is reliable.The data analyzed show that the method can be used as an auxiliary tool with low computational cost for the evaluation of contingencies, providing support for further analysis of the nodes listed as critical.Spearman’s rank correlation coefficient was obtained for each centrality calculation and shows a close relation with results from ANAREDE software, with less computational cost and possibility to run high density networks at once.