  The structure of real-world social networks in large part determines the
evolution of social phenomena, including opinion formation, 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, information about global
structure is usually not available to each vertex. Instead, each vertex's
knowledge is generally limited to the locally observable portion of the network
consisting of the subgraph over its immediate neighbors. Such subgraphs, known
as ego networks, have properties that can differ substantially from those of
the global network. In this paper, 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.
