  In numerous physical models on networks, dynamics are based on interactions
that exclusively involve properties of a node's nearest neighbors. However, a
node's local view of its neighbors may systematically bias perceptions of
network connectivity or the prevalence of certain traits. We investigate the
strong friendship paradox, which occurs when the majority of a node's neighbors
have more neighbors than does the node itself. We develop a model to predict
the magnitude of the paradox, showing that it is enhanced by negative
correlations between degrees of neighboring nodes. We then show that by
including neighbor-neighbor correlations, which are degree correlations one
step beyond those of neighboring nodes, we accurately predict the impact of the
strong friendship paradox in real-world networks. Understanding how the paradox
biases local observations can inform better measurements of network structure
and our understanding of collective phenomena.
