Suppose that the spectrum of Laplacian matrix of the

directed graph with spanning tree is

The fact that the edge connecting node A to node B with no requirement for feedback is the reason for application of

directed graph in developing automation for management processes, since in description, analysis and synthesis of automation for process management feedbackis not always necessary.

We can represent an automaton as a

directed graph. Each state is represented as a vertex, and the effect of each letter on each state is represented as a directed edge.

Definition: 2.2 Neutrosophic

directed graph: A neutrosophic

directed graph is a

directed graph which has at least one edge to be indeterminacy.

First, it executes the aggregating algorithm for compressing different granularity data; it then executes the graph algorithm to build the

directed graph with respect to paths of object movements; finally, it completes the preprocessing of uncertain data.

The topology of M2M network is modeled as a

directed graph, G(V, E), where V and E are set of nodes and set of links, respectively, with the following properties.

As described herein, we tested a random walk model that presents a network of proteins as a

directed graph with a restarting point and used stationary distribution to predict the potential impact of each protein in this network on p53-MDM2 interaction.

This is the

directed graph on vertex set [{0, 1, ..., q - 1}.sup.n], the set of all strings of length n over an alphabet of size q, whose directed edges go from each vertex [x.sub.1] ...

Given a

directed graph G with vertices [v.sub.i], ..., [v.sub.l], the adjacency matrix of G is an (l x l)-matrix A(G) = [[a.sub.ij]] where [a.sub.ij] = 1 if there is an edge directed from [v.sub.i] to [v.sub.j], and [a.sub.ij] = 0 otherwise.

Given a flow network, that is a

directed graph G = (V, E) with source s and sink t (a sink is the node in a network that captures the information flow), where edge (u, v) has capacity c (u, v) > 0, flow f (u,v) > =0 and cost a (u,v), the cost of sending this flow is f(u,v) * a (u,v); s and t are nodes of the network (e.g.