Topic
Cycle graph
About: Cycle graph is a research topic. Over the lifetime, 897 publications have been published within this topic receiving 21788 citations. The topic is also known as: circular graph.
Papers published on a yearly basis
1 / 2
Papers
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.
9,498 citations
TL;DR: An assortment of methods for finding and counting simple cycles of a given length in directed and undirected graphs improve upon various previously known results.
Abstract: We present an assortment of methods for finding and counting simple cycles of a given length in directed and undirected graphs. Most of the bounds obtained depend solely on the number of edges in the graph in question, and not on the number of vertices. The bounds obtained improve upon various previously known results.
742 citations
TL;DR: The probability that a random graph with n vertices and cn log n edges contains a Hamiltonian circuit tends to 1 as n -> ~ (if c is sufficiently large).
583 citations
TL;DR: An implementation of the algorithm which runs in 0(m logn) time if the problem graph has n vertices and m edges is given, and a modification for dense graphs gives a running time of 0(n2).
Abstract: Chu and Liu, Edmonds, and Bock have independently devised an efficient algorithm to find an optimum branching in a directed graph. We give an implementation of the algorithm which runs in 0(m logn) time if the problem graph has n vertices and m edges. A modification for dense graphs gives a running time of 0(n2). We also show that the unmodified algorithm runs in 0(n(log n)2 +m) time on an average graph, assuming a uniform probability distribution.
423 citations
13 Oct 1975
TL;DR: In this article, a new algorithm for finding a maximum matching in an arbitrary graph was proposed, which has a complexity of O(n 2.5) and O(m √n?log n) where n, m are the numbers of the vertices and the edges in the graph.
Abstract: This work presents a new efficient algorithm for finding a maximum matching in an arbitrary graph. Two implementations are suggested, the complexity of the first is O(n2.5) and the complexity of the second is O(m√n?log n) where n, m are the numbers of the vertices and the edges in the graph.
329 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 19 |
| 2020 | 14 |
| 2019 | 20 |
| 2018 | 15 |
| 2017 | 28 |
| 2016 | 34 |