Infection Spread on a Network (Graph Propagation)

You are given a network (graph) and an initial set of infected nodes. Under the propagation rules provided by the interviewer, simulate or compute the infection outcome. Implement a function/program to output the requested result (e.g., earliest infection time for each node, nodes infected at step T, total infected count, or whether a target node becomes infected). Note: The source only mentions the keyword “infection” without precise I/O and rules; this is a reconstructable problem skeleton.