  Adoption processes in socio-technological systems have been widely studied
both empirically and theoretically. The way in which social norms, behaviors,
and even items such as books, music, or other commercial or technological
product spread in a population is usually modeled as a process of social
contagion, in which the agents of a social system can infect their neighbors on
the underlying network of social contacts. More recently, various models have
also been proposed to reproduce the typical dynamics of a process of discovery,
in which an agent explores a space of relations between ideas or items in
search for novelties. In both types of processes, the structure of the
underlying networks, respectively, the network of social contacts in the first
case, and the network of relations among items in the second one, plays a
fundamental role. However, the two processes have been traditionally seen and
studied independently. Here, we provide a brief overview of the existing models
of social spreading and exploration and of the latest advancements in both
directions. We propose to look at them as two complementary aspects of the same
adoption process: on the one hand, there are items spreading over a social
network of individuals influencing each other, and on the other hand,
individuals explore a network of similarities among items to adopt. The
two-fold nature of the approach proposed opens up new stimulating challenges
for the scientific community of network and data scientists. We conclude by
outlining some possible directions that we believe may be relevant to be
explored in the coming years.
