Dynamic processes that can be described in a stochastic manner by random walk strategies are ubiquitous. This chapter introduces some basic features of "Markovian" random walks on connected undirected graphs. It explains the basic properties of Markov chains. A random walk that is performed on a ...
首先考虑undirected connected unweighted graphs: 那么有adjacency matrix: 令pi(t) 为在t 时刻走到节点 i 上的概率,那么有 矩阵形式为: 那么有 图上的随机游走会收敛到一个limiting distribution (stationary distribution): Physics of Diffusion 2 Diffusion on graph 令\Phi(r,t) 是浓度(concentration),那么有...
undirected graph. A random walk on a graph is a process that begins at some vertex, and at each time step moves to another vertex. When the graph is unweighted, the vertex the walk moves to is chosen uniformly at random among the neighbors of the present vertex. When the graph is ...
Standard Random Walk on an undirected graph, and the invariant/stationary distribution. Lecture 13b of a semester-long graduate course on math and CS fundamentals for research in theoretical computer science, taught at Carnegie Mellon University. ...
there is still a phase transition on the time that the epidemic ends, which can be either very early or very late. Let\(G=([n],E)\)be an undirected finite and connected graph onnvertices,Aits adjacency matrix, and\(\rho (A)\)its spectral radius. Let\(\tau \)denote the time that...
IfthegraphisundirectedA(i,j)=A(j,i),i.e.Aissymmetric nxnTransitionmatrixP.PisrowstochasticP(i,j)=probabilityofsteppingonnodejfromnodei =A(i,j)/∑iA(i,j)nxnLaplacianMatrixL.L(i,j)=∑iA(i,j)-A(i,j)Symmetricpositivesemi-definiteforundirectedgraphsSingular ...
•Givenanundirected,connectedgraphG(V,E)with|V|=n,|E|=marandom“step”inGisamovefromsomenodeutoarandomlyselectedneighborv.Arandomwalkisasequenceoftheserandomstepsstartingfromsomeinitialnode.5 43 6 2 1G Pointstonote •Processesisdiscrete•Gisnotnecessarilyplanar•Gisnotnecessarilyfullyconnected•A...
•Givenanundirected,connectedgraphG(V,E)with|V|=n,|E|=marandom“step”inGisamovefromsomenodeutoarandomlyselectedneighborv.Arandomwalkisasequenceoftheserandomstepsstartingfromsomeinitialnode.5 43 6 2 1G Pointstonote •Processesisdiscrete•Gisnotnecessarilyplanar•Gisnotnecessarilyfullyconnected•A...
A brief survey of the physical relevance of the notion of random walk on both undirected and directed graphs is given followed by the exposition of some... P Erdős,RL Graham 被引量: 18发表: 2013年 Fast Random Walks on Finite Graphs and Graph Topological Information A random walk on a ...
2.2 Parameters to be considered in the evolution of classical random walk Given an undirected graph G(V,E), where ‘V’ and ‘E’ are the set of vertices and edges respectively, a random walk on graph G considers the following parameters to measure the efficiency of this walk. 2.2.1 Acc...