Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSpectral properties of the Google matrix of the World Wide Web and other directed networks
226
0
0.0
(
0
)
Added by
Bertrand Georgeot
Publication date
2010
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure in the vicinity of the maximal eigenvalue for Google damping parameter $alpha$ equal to unity. The vocabulary networks have relatively homogeneous spectral density, while university networks have pronounced spectral structures which change from one university to another, reflecting specific properties of the networks. We also determine specific properties of eigenstates of the Google matrix, including the PageRank. The fidelity of the PageRank is proposed as a new characterization of its stability.
rate research
Read More
We study the properties of the Google matrix of an Ulam network generated by intermittency maps. This network is created by the Ulam method which gives a matrix approximant for the Perron-Frobenius operator of dynamical map. The spectral properties of eigenvalues and eigenvectors of this matrix are analyzed. We show that the PageRank of the system is characterized by a power law decay with the exponent $beta$ dependent on map parameters and the Google damping factor $alpha$. Under certain conditions the PageRank is completely delocalized so that the Google search in such a situation becomes inefficient.
We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite size matrix approximant of this operator is constructed by the Ulam method. This method applied to the simple dynamical model creates the directed Ulam networks with approximate scale-free scaling and characteristics being rather similar to those of the World Wide Web. The simple dynamical attractors play here the role of popular web sites with a strong concentration of PageRank. A variation of the Google parameter $alpha$ or other parameters of the dynamical map can drive the PageRank of the Google matrix to a delocalized phase with a strange attractor where the Google search becomes inefficient.
We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different value of correlation among their entries. Spectra of random networks, with completely uncorrelated entries show a circular distribution with delocalized eigenvectors, where as networks with correlated entries have localized eigenvectors. In order to understand the origin of localization we track the spectra as a function of connection probability and directionality. As connections are made directed, eigenstates start occurring in complex conjugate pairs and the eigenvalue distribution combined with the localization measure shows a rich pattern. Moreover, for a very well distinguished community structure, the whole spectrum is localized except few eigenstates at boundary of the circular distribution. As the network deviates from the community structure there is a sudden change in the localization property for a very small value of deformation from the perfect community structure. We search for this effect for the whole range of correlation strengths and for different community configurations. Furthermore, we investigate spectral properties of a metabolic network of zebrafish, and compare them with those of the model networks.
Motives or goals are recognized in psychology literature as the most fundamental drive that explains and predicts why people do what they do, including when they browse the web. Although providing enormous value, these higher-ordered goals are often unobserved, and little is known about how to leverage such goals to assist peoples browsing activities. This paper proposes to take a new approach to address this problem, which is fulfilled through a novel neural framework, Goal-directed Web Browsing (GoWeB). We adopt a psychologically-sound taxonomy of higher-ordered goals and learn to build their representations in a structure-preserving manner. Then we incorporate the resulting representations for enhancing the experiences of common activities people perform on the web. Experiments on large-scale data from Microsoft Edge web browser show that GoWeB significantly outperforms competitive baselines for in-session web page recommendation, re-visitation classification, and goal-based web page grouping. A follow-up analysis further characterizes how the variety of human motives can affect the difference observed in human behavioral patterns.
We construct the Google matrix of the entire Twitter network, dated by July 2009, and analyze its spectrum and eigenstate properties including the PageRank and CheiRank vectors and 2DRanking of all nodes. Our studies show much stronger inter-connectivity between top PageRank nodes for the Twitter network compared to the networks of Wikipedia and British Universities studied previously. Our analysis allows to locate the top Twitter users which control the information flow on the network. We argue that this small fraction of the whole number of users, which can be viewed as the social network elite, plays the dominant role in the process of opinion formation on the network.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
