  Many social, technological and biological interactions involve network
relationships whose outcome intimately depends on the structure of the network
and on the strengths of the connections. Yet, although much information is now
available concerning the structure of many networks, the strengths are more
difficult to measure. Here we show that, for one particular social network,
notably the e-mail network, a suitable measure of the strength of the
connections can be available. We also propose a simple mechanism, based on
positive feedback and reciprocity, that can explain the observed behavior and
that hints toward specific dynamics of formation and reinforcement of network
connections. Network data from contexts different from social sciences indicate
that power-law, and generally broad, distributions of the connection strength
are ubiquitous, and the proposed mechanism has a wide range of applicability.
