The Treaty of Lisbon strengthened the role of national parliaments in the European Union. It introduced an 'early warning system', granting parliamentary chambers the right to reject legislative proposals by the European Commission. Previous studies assumed independence between the decisions of parliaments to reject a legislative proposal. We apply recent advances in inferential network analysis and argue that parliamentary vetoes are better explained by conceptualizing parliaments' veto actions as a temporal network. Network effects can be observed along the dimension of party families. Based on a new permutation approach, we find that parliaments with similar party majorities influence each other over the course of the decision period ('social influence'), rather than basing their decisions independently on joint prior partisanship ('selection').