Motivated by new evidence from the 2023 U.S. regional bank crisis, I develop a theory of how depositor social structure influences bank runs. Rumors about bank financial health spread via interpersonal communication, triggering withdrawals that may lead to collapse. I show that the occurrence, speed, and scale of runs depend on depositor connectedness—the likelihood that agents know and communicate with each other. Higher connectedness accelerates information spread, making runs faster and more severe. In contrast, dispersed depositor bases slow down runs, and can even prevent them entirely.

Can fact-checking improve communication in a network? I study a communication network where agents can publicly commit ex-ante to fact-check any message they send with a reliability of their choice. I show that truth-seeking agents use fact-checking as a device to verify information while biased agents—who want false opinions to spread—use fact-checking as a persuasion device to improve their credibility. I describe how a designer can implement full communication (all messages are trusted and transmitted) by choosing an appropriate cost for fact-checking commitment, to be paid by agents. Finally, I study who carries the "burden of proof"; that which agents bear the necessary fact-checking to ensure sufficient trust in the network. I show that when the cost of fact-checking is low, unbiased agents carry the "burden of proof." Conversely, when the cost is high, biased agents carry it.