  In this paper, we study how rumors in Online Social Networks (OSNs) may
impact the performance of device-to-device (D2D) communication. As D2D is a new
technology, people may choose not to use it when believed in rumors of its
negative impacts. Thus, the cellular network with underlaying D2D is vulnerable
to OSNs as rumors in OSNs may decrement the throughput of the cellular network
in popular content delivery scenarios. To analyze the vulnerability, we
introduce the problem of finding the most critical nodes in the OSN such that
the throughput of a content delivery scenario is minimized when a rumor starts
from those nodes. We then propose an efficient solution to the critical nodes
detection problem. The severity of such vulnerability is supported by extensive
experiments in various simulation settings, from which we observe up to $40\%$
reduction in network throughput.
