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This book represents Alina Stoica's PhD dissertation. The main goal of the research was to characterize individuals connected in a social network by analyzing the local structure of the graph. For that, a method that describes the way nodes are embedded in the network was proposed. The method is related to the analysis of egocentred networks in sociology and to the local approach in the study of complex graphs. It can be applied to small networks, to fractions of networks and also to large networks, due to its small complexity. The proposed method was applied to two large social networks, one modeling online activity on MySpace, the other one modeling mobile phone communications. In the first case, the goal was to analyze the online popularity of artists on MySpace. In the second case, a new method for clustering nodes that are connected in a similar way to the network was introduced. Although in this thesis the two proposed methods were used only for social networks, they can beapplied in the same way to any other graph, no matter its origin.