Existing wireless sensor networks（ WSNs） clustering algorithm neglects problems such as uneven communication cost between a cluster head and cluster members and‘isolated cluster heads’. In view of this

a mobile clustering protocol based on force model is proposed

which considers both node residual energy and node density while cluster head is electing; in order to further balance communication cost between a cluster head and cluster members

the protocol allows cluster head node to move adaptively according to force model related to residual energy of cluster members and distances after cluster head election. Furthermore

relay node election algorithm is proposed to obtain full connection between nodes of cluster heads. Experimental results show that the protocol can effectively balance network energy consumption and further improve network stability.