Based on graph theory,the directed graph is mapped to the directed communication network;the problem of broadcasting-time for directed communication network is studied.

In order to perfect the theories of the dynamic core and its application in the traffic management system,the methods of calculating the core and coritivity of the directional connected network system are proposed.

Based on non-uniform swarm,a dynamic model in directed networks was constructed.

The deformed Floyd algorithm of the shortest path between the two nodes in the directed networks is presented and the complexity of time shares the same rank with Floyd algorithm,but it reveals an object image and provides an easy way to programme.

So far, few of researches have focused on the theory and application of directed networks, and most of them treated directed networks as a na?ve extension of undirected networks .

May be studied as the weighted directed network system.

The two-way search algorithm for finding the shortest path between two vertexes in a directed network in this paper is proposed.

In this paper, we study the propeties of the spanning incoming tree in a digraph network, and propose a simple algorithm for finding the minimum spanning incoming tree in a digraph network, we also present an example for applying this algorithm.