Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0110338

Curvature of Co-Links Uncovers Hidden Thematic Layers in the World Wide Web

Jean-Pierre Eckmann·Elisha Moses
View original source ↗Read source document ↗Export metadata ↓

Abstract

Beyond the information stored in pages of the World Wide Web, novel types of ``meta-information'' are created when they connect to each other. This information is a collective effect of independent users writing and linking pages, hidden from the casual user. Accessing it and understanding the inter-relation of connectivity and content in the WWW is a challenging problem. We demonstrate here how thematic relationships can be located precisely by looking only at the graph of hyperlinks, gleaning content and context from the Web without having to read what is in the pages. We begin by noting that reciprocal links (co-links) between pages signal a mutual recognition of authors, and then focus on triangles containing such links, since triangles indicate a transitive relation. The importance of triangles is quantified by the clustering coefficient (Watts) which we interpret as a curvature (Gromov,Bridson-Haefliger). This defines a Web-landscape whose connected regions of high curvature characterize a common topic. We show experimentally that reciprocity and curvature, when combined, accurately capture this meta-information for a wide variety of topics. As an example of future directions we analyze the neural network of C. elegans (White, Wood), using the same methods.

Explore related subjects

cond-mat.dis-nncond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jean-Pierre Eckmann, Elisha Moses. 2001-11-30. Curvature of Co-Links Uncovers Hidden Thematic Layers in the World Wide Web. https://doi.org/10.1073/pnas.032093399

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Statistical levels and spatial modes of Fock-space heterogeneity in many-body localization crossovers

Near many-body localization crossovers, local memory fluctuates strongly among eigenstates and ensemble realizations, but the observed heterogeneity combines contributions from different statistical levels. We develop a statistical framework based on configuration-space distance distributions that uses a variance decomposition to separate fluctuations within eigenstates, between eigenstates of one sample, and between samples. Applying this framework to random-cosine and quasiperiodic-cosine Ising ensembles with the same one-site field marginal, we find that, at the exact-diagonalization sizes studied, the clearest difference occurs among disorder realizations or quasiperiodic phase samples, whereas within-eigenstate and within-sample eigenstate-to- eigenstate contributions remain broadly comparable. Spatial covariances show that random outer fluctuations have a much stronger uniform component, whereas quasiperiodic phase fluctuations are organized more strongly at finite wave number and partly cancel in the spatial average controlling the distance center. We find that, near the crossover in the random ensemble, the ensemble-averaged distance center is particularly sensitive to changes in the nominal field strength. Combined with sample-to-sample differences in the realized field amplitude, this mean response accounts for much of the sample-to-sample variation in the distance center. Analysis of half-chain entanglement further shows that its sample-to-sample fluctuations likewise reflect the combined effects of amplitude variations and its own mean response. An application to a fixed-magnetization spin chain demonstrates the framework in a constrained configuration space. Resolving both statistical level and spatial mode therefore provides a more complete picture of sample- dependent many-body memory and its configuration-space probability geometry.

cond-mat.dis-nn↗
arXiv2026

Synchronous and asynchronous Monte Carlo dynamics of mean-field spin glasses with rotationally invariant couplings: what they share and where they differ

We compare two Markov chain Monte Carlo dynamics for Ising spin glasses with rotationally invariant couplings: the synchronous Monte Carlo method (SyncMC), which updates all spins in parallel with the help of Gaussian auxiliary fields, and asynchronous Metropolis-Hastings dynamics, which updates one spin at a time. Using the Guionnet-Maïda formula, we derive the dynamical mean-field theory of both dynamics in terms of the R-transform of the coupling spectrum. The two effective single-spin processes share a retarded self-interaction and a Gaussian noise; SyncMC has, in addition, an instantaneous self-coupling and a noise that depends only on the response function. These additional terms act only on the fastest time scale, so that the equations for slow time scales, including the fluctuation-dissipation ratio and, for the Sherrington-Kirkpatrick model, the Parisi equation, are the same for the two dynamics. Simulations of the random orthogonal and Sherrington-Kirkpatrick models confirm that both dynamics approach the same fluctuation-dissipation relations, differing only in how many updates they need to do so.

cond-mat.dis-nn↗
arXiv2026

Optical Ceiling on Polaron Mobility in Disordered Molecular Semiconductors: Lessons from Eumelanin

Polaron hopping in disordered molecular semiconductors such as eumelanin is set by energetic disorder $σ$ and reorganization energy $λ$. We show that the reduced polaron absorption band encodes this transport problem. Its value at zero energy fixes the mean hop rate, which bounds the mobility in any dimension. For Gaussian disorder and classical vibrations its centroid is $E_\mathrm{op}=λ+(1-c)σ^2/k_BT$, its variance obeys the Hush relation, and the bound is the Marcus rate at $λ\to E_\mathrm{op}$; a 1D lower bound vanishes at $k_BT^*=(1-c)σ^2/λ$, read from optics.

cond-mat.dis-nn↗