Journal ArticleDOI
Some further development on the eigensystem approach for graph isomorphism detection
P. R. He,Wenjun Zhang,Q. Li +2 more
TLDR
A new matrix called adjusted adjacency matrix is proposed that meets the requirement that a graph must contain at least one distinct eigenvalue and is shown to be not only effective but also more efficient than that based on the adjACency matrix.Abstract:
Many science and engineering problems can be represented by a network, a generalization of which is a graph. Examples of the problems that can be represented by a graph include: cyclic sequential circuit, organic molecule structures, mechanical structures, etc. The most fundamental issue with these problems (e.g., designing a molecule structure) is the identification of structure, which further reduces to be the identification of graph. The problem of the identification of graph is called graph isomorphism. The graph isomorphism problem is an NP problem according to the computational complexity theory. Numerous methods and algorithms have been proposed to solve this problem. Elsewhere we presented an approach called the eigensystem approach. This approach is based on a combination of eigenvalue and eigenvector which are further associated with the adjacency matrix. The eigensystem approach has been shown to be very effective but requires that a graph must contain at least one distinct eigenvalue. The adjacency matrix is not shown sufficiently to meet this requirement. In this paper, we propose a new matrix called adjusted adjacency matrix that meets this requirement. We show that the eigensystem approach based on the adjusted adjacency matrix is not only effective but also more efficient than that based on the adjacency matrix.read more
Citations
More filters
Journal ArticleDOI
Isomorphism identification of graphs : Especially for the graphs of kinematic chains
Huafeng Ding,Zhen Huang +1 more
TL;DR: In this article, a unique representation of a graph, the characteristic adjacency matrix, is derived from all the loops of the graph obtained through a new algorithm, and the canonical perimeter graph is obtained by relabelling the perimeter graph.
Journal ArticleDOI
Backtrackless Walks on a Graph
TL;DR: Efficient methods for computing graph kernels, which are based on backtrackless walks in a labeled graph and whose worst case running time is the same as that of kernels based on random walks are presented.
Journal ArticleDOI
The Establishment of the Canonical Perimeter Topological Graph of Kinematic Chains and Isomorphism Identification
Huafeng Ding,Zhen Huang +1 more
TL;DR: In this paper, a one-to-one descriptive method, the canonical adjacency matrix set of kinematic chains, is proposed to identify isomorphism of chains.
Journal ArticleDOI
Similarity recognition and isomorphism identification of planar kinematic chains
TL;DR: A set of SRII methods is proposed based on the graph theory definition of similarity and isomorphism, appropriate for planar single and multiple joints KCs, planetary gear trains, contracted graphs, and multicolor graphs, which are in agreement with those in the cited literature.
Journal ArticleDOI
Improving Neural Networks for Mechanism Kinematic Chain Isomorphism Identification
TL;DR: A new algorithm based on a competitive Hopfield network is developed for automatic computation in the kinematic chain isomorphism problem, which provides directly interpretable solutions and does not demand tuning of parameters.
References
More filters
Book
Non-negative Matrices and Markov Chains
TL;DR: Finite Non-Negative Matrices as mentioned in this paper are a generalization of finite stochastic matrices, and finite non-negative matrices have been studied extensively in the literature.
Journal ArticleDOI
The graph isomorphism disease
Ronald C. Read,Derek G. Corneil +1 more
TL;DR: The present state of the art of isomorphism testing is surveyed, its relationship to NP-completeness is discussed, and some of the difficulties inherent in this particularly elusive and challenging problem are indicated.
Related Papers (5)
A new method to mechanism kinematic chain isomorphism identification
An artificial neural network approach to mechanism kinematic chain isomorphism identification
F.G. Kong,Q. Li,Wenjun Zhang +2 more