Community detection aims to identify the cohesive vertex sets in a network. It is widely used in many domains, e.g., World Wide Web, online social networks, and communication networks. Many clustering models are proposed in the literature. However, most of them are designed directly on the original structure of a network, they usually achieve low accuracy in practice, since real-world networks are presenting fuzzy community structures. Recently, higher-order network units are introduced to community detection, these models typically define a higher-order hypergraph, where communities are extracted. Although the higher-order models are effective in terms of accuracy, many essential edges are completely eliminated or trivialized in the hypergraph. To address the problem, we propose a novel connectivity pattern with a mixture of standard edges and higher-order connections, whereby we define biased personalized PageRank diffusion for local community detection and develop a local approach to compute the PageRank vectors. Moreover, we present a higher-order seeding strategy to derive the starting seeds. Extensive experiments demonstrate that the proposed framework largely outperforms the approaches in the state of the art in terms of accuracy.