Topic

# Directed graph

About: Directed graph is a research topic. Over the lifetime, 12277 publications have been published within this topic receiving 302476 citations. The topic is also known as: digraph.

##### Papers published on a yearly basis

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TL;DR: In this paper, the authors present a data structure for representing Boolean functions and an associated set of manipulation algorithms, which have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large.

Abstract: In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. We present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of our approach.

9,021 citations

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TL;DR: A new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains, and implements a function tau(G,n) isin IRm that maps a graph G and one of its nodes n into an m-dimensional Euclidean space.

Abstract: Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) isin IRm that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

5,701 citations

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TL;DR: The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples of an improved version of an algorithm for finding the strongly connected components of a directed graph.

Abstract: The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected componen...

5,660 citations

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TL;DR: This experiment demonstrates the feasibility of carrying out computations at the molecular level by solving an instance of the directed Hamiltonian path problem with standard protocols and enzymes.

Abstract: The tools of molecular biology were used to solve an instance of the directed Hamiltonian path problem. A small graph was encoded in molecules of DNA, and the "operations" of the computation were performed with standard protocols and enzymes. This experiment demonstrates the feasibility of carrying out computations at the molecular level.

4,266 citations

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TL;DR: The World-Wide Web becomes a large directed graph whose vertices are documents and whose edges are links that point from one document to another, which determines the web's connectivity and consequently how effectively the authors can locate information on it.

Abstract: Despite its increasing role in communication, the World-Wide Web remains uncontrolled: any individual or institution can create a website with any number of documents and links. This unregulated growth leads to a huge and complex web, which becomes a large directed graph whose vertices are documents and whose edges are links (URLs) that point from one document to another. The topology of this graph determines the web's connectivity and consequently how effectively we can locate information on it. But its enormous size (estimated to be at least 8×108 documents1) and the continual changing of documents and links make it impossible to catalogue all the vertices and edges.

4,135 citations