  Temporal networks are widely used to represent a vast diversity of systems,
including in particular social interactions, and the spreading processes
unfolding on top of them. The identification of structures playing important
roles in such processes remains largely an open question, despite recent
progresses in the case of static networks. Here, we consider as candidate
structures the recently introduced concept of span-cores: the span-cores
decompose a temporal network into subgraphs of controlled duration and
increasing connectivity, generalizing the core-decomposition of static graphs.
To assess the relevance of such structures, we explore the effectiveness of
strategies aimed either at containing or maximizing the impact of a spread,
based respectively on removing span-cores of high cohesiveness or duration to
decrease the epidemic risk, or on seeding the process from such structures. The
effectiveness of such strategies is assessed in a variety of empirical data
sets and compared to baselines that use only static information on the
centrality of nodes and static concepts of coreness, as well as to a baseline
based on a temporal centrality measure. Our results show that the most stable
and cohesive temporal cores play indeed an important role in epidemic processes
on temporal networks, and that their nodes are likely to represent influential
spreaders.
