Event-based summarization attempts to select and organize the sentences in a summary with respect to the events or the sub-events that the sentences describe. Each event has its own internal structure, and meanwhile often relates to other events semantically, temporally, spatially, causally or conditionally. In this paper, we define an event as one or more event terms along with the named entities associated, and present a novel approach to derive intra- and inter- event relevance using the information of internal association, semantic relatedness, distributional similarity and named entity clustering. We then apply PageRank ranking algorithm to estimate the significance of an event for inclusion in a summary from the event relevance derived. Experiments on the DUC 2001 test data shows that the relevance of the named entities involved in events achieves better result when their relevance is derived from the event terms they associate. It also reveals that the topic-specific relevance ...