What is the difference between attractor and recurrent network? How are attractor and recurrent networks related? Is attractor network is private case of recurrent? Is there a mathematical formalism that defines both rigorously as graphs?
Many recurrent networks have attractors. For example, the BAM (bidirectional associative network) is a recurrent network: one input is presented and the network cycles until no more changes are seen in the connection weights. The BAM can be understood as developing attractor states: Seen in n-dimensions (in which n is the number of units in the model), the state can be seen as a position. Whenever the same stimuli is presented, the state of the network will stabilize to the same position. 

One reference is Chartier S, Boukadoum M. (2006) A bidirectional heteroassociative memory for binary and grey-level patterns. IEEE Transactions on Neural Networks, 17(2):385-96.