We generalize bounded-confidence models (BCMs) of opinion dynamics by incorporating neighborhood effects. In a BCM, interacting agents influence each other through dyadic influence if their opinions are sufficiently similar to each other. In our "neighborhood BCMs" (NBCMs), interacting agents are influenced both by each other's opinions and by the opinions of the agents in each other's neighborhoods. Our NBCMs thus include both the usual dyadic influence between agents and a "transitive influence", which encodes the influence of an agent's neighbors, when determining whether or not an interaction changes the opinions of agents. In this transitive influence, an individual's opinion is influenced by a neighbor when, on average, the opinions of the neighbor's neighbors are sufficiently similar to its own opinion. We formulate both neighborhood Deffuant--Weisbuch (NDW) and neighborhood Hegselmann--Krause (NHK) BCMs. We build further on our NBCMs by introducing a neighborhood-based network adaptation in which a network coevolves with agent opinions by changing its structure through "transitive homophily". In this network evolution, an agent breaks a tie to one of its neighbors and then rewires that tie to a new agent, with a preference for agents with a mean neighbor opinion that is closer to its own opinion. Using numerical simulations on a variety of types of networks, we explore how the qualitative opinion dynamics and network properties of our adaptive NDW model change as we adjust the relative proportions of dyadic and transitive influence. In our numerical experiments, we find that incorporating neighborhood effects into the opinion dynamics and the network-adaptation rewiring strategy tends to reduce the spectral gap and degree assortativity of networks. (This is a shortened version of the paper's abstract.)