这里我们假设函数并不会对Graph的链接性造成影响,我们只是假设根据图返回性质。 此外,Graph的边天然的导致在一些函数中会有局部性限制(locality constraint),比如CNN在图像中的局部进行卷机运算,GCN也只能在一些节点的邻居节点(neighbourhood of a node),邻居节点的定义为: $$N_u={v|(u,v)\in E}$$ ![1677128...
connected grapheigenvalue distributionplanar graphserial structureThis paper describes the previously unknown statistical distribution of adjacency matrix spectra for planar graphs, also known as spatial weights matrices, in terms of the following three readily available eigenvalue properties: extremes, rank ...
求高手帮忙翻译下英文文献in this paper,we consider only simple connected graphs and follow the notationof [1].Let G be a simple graph with vertex set V(G) and edge set E(G). Theadjacency matrix of G is A(G) = (J), where J = 1 if two vertic
For any real α∈[0,1], Nikiforov defined the Aα-matrix of a graph G as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and the diagonal matrix of vertex degrees of G, respectively. The largest eigenvalue of Aα(G) is called the α-index ...
Graph schematic forL= 10 alongside adjacency matrix forL = 100 is provided. System sizes are coded by colour.a–fAnti-ferromagnetic orderCAFM,XYorderCXY, magnetisation density\(\langle {\hat{S}}^{z}\rangle /L\), von-Neumann entanglement entropy between sitesV = 1. . . L...
The Aα matrix of a graph G is defined by Nikiforov as Aα(G)=αD(G)+(1α)A(G), where α∈[0,1], A(G) and D(G) respectively denotes the adjacency matrix and the degree diagonal matrix of G. The eigenvalues of Aα(G) are called the Aα-eigenvalues of G. In this paper...
node_a.subtree# returns a GenericGraph based on all nodes reachable from `node_a`# => #<Connected::GenericGraph:0x00007f...node_a.subtree.radius# => 4node_a.subtree.diameter# => 7node_a.subtree.adjacency_matrix# => Matrix[[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 0]...
For two disjoint subsets S,T⊂V(G), we denote the induced bipartite graph between S and T by G[S,T]. Let D(G) and A(G) be the diagonal matrix of the degrees and the adjacency matrix of G, respectively. Then Q(G)=D(G)+A(G) is the signless Laplacian matrix of G. The ...
摘要: Summary: We give a necessary and sufficient condition for a graph to be bipartite in terms of an eigenvector corresponding to the largest eigenvalue of the adjacency matrix of the graph.关键词:Graph Bipartite Principal eigenvector Independent set ...
It's obvious that the graph above is connected. In the third test case, if we do the operation with vertex333and444, we will get the following graph represented by an adjacency matrix: [0111101111011110]\begin{bmatrix} 0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0 \end{bmatrix}...