  We describe and develop three recent novelties in network research which are
particularly useful for studying social systems. The first one concerns the
discovery of some basic dynamical laws that enable the emergence of the
fundamental features observed in social networks, namely the nontrivial
clustering properties, the existence of positive degree correlations and the
subdivision into communities. To reproduce all these features we describe a
simple model of mobile colliding agents, whose collisions define the
connections between the agents which are the nodes in the underlying network,
and develop some analytical considerations. The second point addresses the
particular feature of clustering and its relationship with global network
measures, namely with the distribution of the size of cycles in the network.
Since in social bipartite networks it is not possible to measure the clustering
from standard procedures, we propose an alternative clustering coefficient that
can be used to extract an improved normalized cycle distribution in any
network. Finally, the third point addresses dynamical processes occurring on
networks, namely when studying the propagation of information in them. In
particular, we focus on the particular features of gossip propagation which
impose some restrictions in the propagation rules. To this end we introduce a
quantity, the spread factor, which measures the average maximal fraction of
nearest neighbors which get in contact with the gossip, and find the striking
result that there is an optimal non-trivial number of friends for which the
spread factor is minimized, decreasing the danger of being gossiped.
