  A rumor spreading in a social network or a disease propagating in a community
can be modeled as an infection spreading in a network. Finding the infection
source is a challenging problem, which is made more difficult in many
applications where we have access only to a limited set of observations. We
consider the problem of estimating an infection source for a
Susceptible-Infected model, in which not all infected nodes can be observed.
When the network is a tree, we show that an estimator for the source node
associated with the most likely infection path that yields the limited
observations is given by a Jordan center, i.e., a node with minimum distance to
the set of observed infected nodes. We also propose approximate source
estimators for general networks. Simulation results on various synthetic
networks and real world networks suggest that our estimators perform better
than distance, closeness, and betweenness centrality based heuristics.
