Related papers: Quantifying structure in networks
We construct tree-decompositions of graphs that distinguish all their k-blocks and tangles of order k, for any fixed integer k. We describe a family of algorithms to construct such decompositions, seeking to maximize their diversity subject…
The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
Analyzing the geometry of correlation sets constrained by general causal structures is of paramount importance for foundational and quantum technology research. Addressing this task is generally challenging, prompting the development of…
We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…
We develop a new class of random graph models for the statistical estimation of network formation -- subgraph generated models (SUGMs). Various subgraphs -- e.g., links, triangles, cliques, stars -- are generated and their union results in…
Any network studied in the literature is inevitably just a sampled representative of its real-world analogue. Additionally, network sampling is lately often applied to large networks to allow for their faster and more efficient analysis.…
This paper describes a new approach to the problem of the structural research of clusters based on the theory of geodetic and k-geodetic graphs. We firmly believe that this same approach can be used when solving problems of correlation…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…
Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…
The local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network. The clustering coefficient, reflecting the local configuration of triangles, can be seen as a special case of this…
The organisation of a network in a maximal set of nodes having at least $k$ neighbours within the set, known as $k$-core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost $k$-shells…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
Our recent paper [Grauwin et al. Sci. Rep. 7 (2017)] demonstrates that community and hierarchical structure of the networks of human interactions largely determines the least and should be taken into account while modeling them. In the…