  In recent years, researchers proposed several algorithms that compute metric
quantities of real-world complex networks, and that are very efficient in
practice, although there is no worst-case guarantee.
  In this work, we propose an axiomatic framework to analyze the performances
of these algorithms, by proving that they are efficient on the class of graphs
satisfying certain axioms. Furthermore, we prove that the axioms are verified
asymptotically almost surely by several probabilistic models that generate
power law random graphs, such as the In recent years, researchers proposed
several algorithms that compute metric quantities of real-world complex
networks, and that are very efficient in practice, although there is no
worst-case guarantee.
  In this work, we propose an axiomatic framework to analyze the performances
of these algorithms, by proving that they are efficient on the class of graphs
satisfying certain properties. Furthermore, we prove that these properties are
verified asymptotically almost surely by several probabilistic models that
generate power law random graphs, such as the Configuration Model, the Chung-Lu
model, and the Norros-Reittu model. Thus, our results imply average-case
analyses in these models.
  For example, in our framework, existing algorithms can compute the diameter
and the radius of a graph in subquadratic time, and sometimes even in time
$n^{1+o(1)}$. Moreover, in some regimes, it is possible to compute the $k$ most
central vertices according to closeness centrality in subquadratic time, and to
design a distance oracle with sublinear query time and subquadratic space
occupancy.
  In the worst case, it is impossible to obtain comparable results for any of
these problems, unless widely-believed conjectures are false.
