  A common way of classifying network connectivity is the association of the
nodal degree distribution to specific probability distribution models. During
the last decades, researchers classified many networks using the Poisson or
Pareto distributions. Urban infrastructures, like transportation (railways,
roads, etc.) and distribution (gas, water, energy, etc.) systems, are peculiar
networks strongly constrained by spatial characteristics of the environment
where they are constructed. Consequently, the nodal degree of such networks
spans very small ranges not allowing a reliable classification using the nodal
degree distribution. In order to overcome this problem, we here (i) define the
neighborhood degree, equal to the sum of the nodal degrees of the nearest
topological neighbors, the adjacent nodes and (ii) propose to use neighborhood
degree to classify infrastructure networks. Such neighborhood degree spans a
wider range of degrees than the standard one allowing inferring the
probabilistic model in a more reliable way, from a statistical standpoint. In
order to test our proposal, we here analyze twenty-two real water distribution
networks, built in different environments, demonstrating that the Poisson
distribution generally models very well their neighborhood degree
distributions. This result seems consistent with the less reliable
classification achievable with the scarce information using the standard nodal
degree distribution.
