  Information diffusion, spreading of infectious diseases, and spreading of
rumors are fundamental processes occurring in real-life networks. In many
practical cases, one can observe when nodes become infected, but the underlying
network, over which a contagion or information propagates, is hidden. Inferring
properties of the underlying network is important since these properties can be
used for constraining infections, forecasting, viral marketing, and so on.
Moreover, for many applications, it is sufficient to recover only coarse
high-level properties of this network rather than all its edges. This article
conducts a systematic and extensive analysis of the following problem: Given
only the infection times, find communities of highly interconnected nodes. This
task significantly differs from the well-studied community detection problem
since we do not observe a graph to be clustered. We carry out a thorough
comparison between existing and new approaches on several large datasets and
cover methodological challenges specific to this problem. One of the main
conclusions is that the most stable performance and the most significant
improvement on the current state-of-the-art are achieved by our proposed simple
heuristic approaches agnostic to a particular graph structure and epidemic
model. We also show that some well-known community detection algorithms can be
enhanced by including edge weights based on the cascade data.
