In this paper we explore the connection between evolution algebras, random walks and graphs. More precisely, we study the relationships between the evolution algebra induced by a random walk on a graph and the evolution algebra determined by the same graph. Given that any Markov chain may be ...
1.1.1Sixdegreesofseparationandsocialnetworks...6 1.1.2KevinBaconGameandmovieactornetwork...8 1.1.3Erd˝osnumbersandcollaborationnetworks...9 1.1.4TheWorld-WideWeb...12 1.2Scale-free,small-worldandhighly-clusteredrandomgraphprocesses...15 1.3Talesoftails...17 1.3.1Oldtalesoftails...17 1.3.2...
1.Improved algorithm for minimal feedback arc set based on stochastic evolution;基于随机演化的最小反馈弧集的改进算法 3)randomness of evolution演化随机性 4)random evolving network随机演化网络 1.The random evolving network and BA(Barab si-Albert) scale-free network are unified by introdcing a para...
Random graph generators are necessary tools for many network science applications. For example, the evaluation of graph analysis algorithms requires methods for generating realistic synthetic graphs. Typically random graph generators are generating graphs that satisfy certain global criteria, such as degree ...
Uncovering the role of elementary processes in network evolution. Sci. Rep. 3, 2920 (2013). Scientific Reports | 5:14286 | DOI: 10.1038/srep14286 14 www.nature.com/scientificreports/ 39. Aguirre, J., Papo, D. & Buldú, J. M. Successful strategies for competing networks. Nature Phys. ...
Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de...
We illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We also discuss the threshold function, the giant component, and the evolution of random graphs in this model.William Aiello...
Abstract Exactly what is meant by a ‘complex’ network is not clear; however, what is clear is that it is something other than a random graph. Complex networks arise in a wide range of real social, technological and physical systems. In all cases, the most basic categorization of these ...
Lastly, we study the distribution and the large-scale behavior of the degrees of the vertices; see Theorem 3. 2. Model and results 2.1. Model Let us introduce some notation for (undirected) graphs. Afterwards, we will define the random graph model we will study in the sequel. Definition ...
The molecular graphs can be divided into two categories according to their mutagenicity, that is, their ability to mutate genes of certain bacteria. Figure 2b shows the experimental input projection and evolution of node internal states of a single molecular graph according to the process shown in...