We relax the traditional definition of contact and intercontact times by bringing the notion of vicinity into the game. We propose to analyze disruption-tolerant networks (DTN) under the assumption that nodes are in k-contact when they remain within a few hops from each other and in k-intercontact otherwise (where k is the maximum number of hops characterizing the vicinity). We make interesting observations when analyzing several real-world and synthetic mobility traces. We detect a number of unexpected behaviors when analyzing k-contact distributions; in particular, we observe that in some datasets the average k-contact time decreases as we increase k. In fact, we observe that many nodes spend a non-negligible amount of time in each other's vicinity without coming into direct contact. We also show that a small k (typically between 3 and 4) is sufficient to capture most communication opportunities.