Sudden epidemic infections have the potential of disruption of lives and economy. COVID-19 has provided a recent testimony to this. To prevent spreading of infection, contact tracing is mandatory. However, the contact tracing should be privacy preserving. In a smart city where inhabitants are empowered with body area network (BAN), this contact tracing can be done efficiently by examining the inter-BAN communications (IBC). To avoid tampering of IBCs, blockchain network maintains the IBCs. Contacts can be modeled as a graph. Existing works discuss the use of adjacency matrix for contact tracing in the graph. However, the contact graph may not be a dense graph and can have components in it. As a result, the time taken for determining the contacts of an user can be reduced if the contact tracing is confined within the component (or cluster) to which the user belongs to. The present work proposes a privacy-preserving contact tracing that determines the cluster to which the user belongs to and then finds all its direct and indirect contacts. Security of the proposed scheme has been minutely examined against the possible attacks.