Related papers: Random graph embeddings with general edge potentia…
In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
We introduce a Markov Chain Monte Carlo algorithm which samples from the space of spanning trees of complete graphs using local rewiring operations only. The probability distribution of graphs of this kind is shown to depend on the…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
Network embedding assigns nodes in a network to low-dimensional representations and effectively preserves the network structure. Recently, a significant amount of progresses have been made toward this emerging network analysis paradigm. In…
Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus…
Let $H_d(n,p)$ signify a random $d$-uniform hypergraph with $n$ vertices in which each of the ${n}\choose{d}$ possible edges is present with probability $p=p(n)$ independently, and let $H_d(n,m)$ denote a uniformly distributed with $n$…
Polymer networks invariably possess topological inhomogeneities in the form of loops and dangling ends. The macroscopic properties of such materials are directly dependent on the local cyclic topology around nodes and chains. Here, a new…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
In the field of computer science, the network reliability problem for evaluating the network failure probability has been extensively investigated. For a given undirected graph $G$, the network failure probability is the probability that…
Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. These representations can be used as features for a wide range of tasks on graphs such as classification, clustering, link prediction,…
A remarkable feature of static granular matter is the distribution of force along intricate networks. Even regular inter-particle contact networks produce wildly inhomogeneous force networks where certain "chains" of particles carry forces…
Predicting missing links between entities in a knowledge graph is a fundamental task to deal with the incompleteness of data on the Web. Knowledge graph embeddings map nodes into a vector space to predict new links, scoring them according…
Spectral inference on multiple networks is a rapidly-developing subfield of graph statistics. Recent work has demonstrated that joint, or simultaneous, spectral embedding of multiple independent networks can deliver more accurate estimation…
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…
We consider operators with random potentials on graphs, such as the lattice version of the random Schroedinger operator. The main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…