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In terms of scope and granularity of data, two kinds of connectivity models are broadly in vogue for representing power network data, namely, node-breaker model and bus-branch model. This paper examines both the connectivity models from the perspective of common information model (CIM). Although CIM is primarily designed for most detailed node-breaker representation, with certain extensions CIM can be leveraged to achieve a standard, interoperable bus-branch model representation and exchange format. To facilitate this, it is proposed to introduce new class called TopologyBranch. By decoupling the connectivity information and the equipment parameter information, a mechanism for efficient exchange of time varying system models with minimum information transfer between the power control centers is described in this paper. The proposed CIM bus-branch connectivity model has wide applications in an interoperable, decentralized, hierarchical structure of control centers. Three illustrative examples including one on a practical 20-substation model of the 400 kV transmission network of Maharasthra state, India, are then presented for demonstrating the benefits.