  When investigating the spreading of a piece of information or the diffusion
of an innovation, we often lack information on the underlying propagation
network. Reconstructing the hidden propagation paths based on the observed
diffusion process is a challenging problem which has recently attracted
attention from diverse research fields. To address this reconstruction problem,
based on static similarity metrics commonly used in the link prediction
literature, we introduce new node-node temporal similarity metrics. The new
metrics take as input the time-series of multiple independent spreading
processes, based on the hypothesis that two nodes are more likely to be
connected if they were often infected at similar points in time. This
hypothesis is implemented by introducing a time-lag function which penalizes
distant infection times. We find that the choice of this time-lag strongly
affects the metrics' reconstruction accuracy, depending on the network's
clustering coefficient and we provide an extensive comparative analysis of
static and temporal similarity metrics for network reconstruction. Our findings
shed new light on the notion of similarity between pairs of nodes in complex
networks.
