Structural Properties of Ego Networks

Abstract. The structure of real-world social networks in large part de-termines the evolution of social phenomena, including opinion forma-tion, diffusion of information and influence, and the spread of disease. Globally, network structure is characterized by features such as degree distribution, degree assortativity, and clustering coefficient. However, in-formation about global structure is usually not available to each vertex. Instead, each vertex’s knowledge is generally limited to the locally ob-servable portion of the network consisting of the subgraph over its imme-diate neighbors. Such subgraphs, known as ego networks, have properties that can differ substantially from those of the global network. In this pa-per, we study the structural properties of ego networks and show how they relate to the global properties of networks from which they are derived. Through empirical comparisons and mathematical derivations, we show that structural features, similar to static attributes, suffer from paradoxes. We quantify the differences between global information about network structure and local estimates. This knowledge allows us to better identify and correct the biases arising from incomplete local information.