  Given a set $\Omega$ and a proximity function $\phi: \Omega \times \Omega \to
\mathbb R^+$, we define a new metric for $\Omega$ by considering a path
distance in $\Omega$, that is considered as a complete graph. We analyze the
properties of such a distance, and several procedures for defining the initial
proximity matrix $( \phi(a,b) )_{(a,b) \in \Omega \times \Omega}.$ Our
motivation has its roots in the current interest in finding effective
algorithms for detecting and classifying relations among elements of a social
network. For example, the analysis of a set of companies working for a given
public administration or other figures in which automatic fraud detection
systems are needed. Using this formalism, we state our main idea regarding
fraud detection, that is founded in the fact that fraud can be detected because
it produces a meaningful local change of density in the metric space defined in
this way.
