Trust theory explains how existing social network ties influence trust, but well-publicized examples suggest that even imagined connections can affect it. As extant theory does not explain this phenomenon, we introduce a perceptual network mechanism that elucidates why the ties in our mind influence trustworthiness judgments. We then empirically isolate our novel perceptual mechanism from the known structural network mechanism and compare the two mechanisms’ effects. We do so by focusing on situations where individuals (egos) have incorrect perceptions of others’ (alters’) ties: when egos overlook alters’ existing ties, structural effects on trustworthiness judgments are exposed; when egos imagine alters’ ties, perceptual effects are revealed. Our field study shows that the perceptual effects of imagined advice-giving centrality can be greater than the structural effects of overlooked advice-giving centrality. But perceptual effects diminish when alters are more central in an actual network. Further, we examine the consequences of imagining and overlooking ties. Employees are more willing to be vulnerable to and act as a broker for coworkers who they imagine to be central than those who are actually central but whose ties they overlook.