An event ontology is useful for the semantic integration of heterogeneous datasets related to events. To reduce manual efforts in event ontology construction, several Event-Type Induction (ETI) methods were proposed to automatically find new event types from a given data source. Existing ETI methods utilize a corpus-based data source, and achieve the ETI goal via document clustering over pre-trained neural text embeddings. Most of the ETI methods require a semi-supervised setting to obtain a satisfactory result. In this paper, we improve ETI performance by incorporating graph-based data sources, which usually consists of event nodes, participant subjects/objects and the relational edges. Our motivation is that event type information learned from an event graph can complement that learned from text. This idea leads to the Graph-ETI (G-ETI) algorithm, where event clusters are initially identified from text embeddings and later refined through graph-based label propagation. Our algorithm naturally supports the unsupervised ETI setting where no event types are known beforehand. Moreover, we also provide an LLM-based naming module to generate appropriate names for the new event clusters. In the experiment, our method exhibits better event clustering performance compared to existing baselines, especially in the unsupervised setting. These improved clustering assignments combined with our LLM naming module can lead to high-quality ETI capability, which facilitates the event ontology construction process.