Matroid Structure, Dependencies Based On The Network Data Flow

network coding theory is a break-through in the field of network communication research, and rapidly developed into a important research category after its appearance. Bring far-reaching influence to the fields of information theory, coding theory, communication network, wireless communication, cryptology, operational research, matrix theory etc. now it's becoming a pop research area in the universities all over the world.Matroid is a concept first introduced by the research of linear independency of column vectors of a Matrix, it is a data structure which can reflect the dependency of the elements in a set. The Matroid was used in many fields including linear independency of vectors, graph theory etc since it can abstract the inner relationship of the data.In [18] Randall Dougherty et al analyzed the connection between Matroid and network coding problems, giving a method to get a network from Matroid which preserves some characteristics of the matroid. In this paper we analyze the relationship of the input and output data streams of the network, namely the data dependency, and construct corresponding Matroid of a network. Then we get some characteristics of the network by the character of the Matroid of that network. We give more opinions about the reversibility of the multiple-unicast network. And compare the two different construction procedures.