Related papers: Introducing Loopedia
The Hosoya polynomial of a graph encompasses many of its metric properties, for instance the Wiener index (alias average distance) and the hyper-Wiener index. An expression is obtained that reduces the computation of the Hosoya polynomials…
This paper introduces annotative indexing, a novel framework that unifies and generalizes traditional inverted indexes, column stores, object stores, and graph databases. As a result, annotative indexing can provide the underlying indexing…
We present a novel approach for loop integral reduction in the Feynman parametrization using intersection theory and relative cohomology. In this framework, Feynman integrals correspond to boundary-supported differential forms in the…
Node role explainability in complex networks is very difficult, yet is crucial in different application domains such as social science, neurosciences or computer science. Many efforts have been made on the quantification of hubs revealing…
During routine state space circuit analysis of an arbitrarily connected set of nodes representing a lossless LC network, a matrix was formed that was observed to implicitly capture connectivity of the nodes in a graph similar to the…
In a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolation-like emergence of a macroscopic observable component in graphs in which the state of a fraction of…
Graph database systems are increasingly adapted for storing and processing heterogeneous network-like datasets. However, due to the novelty of such systems, no standard data model or query language has yet emerged. Consequently, migrating…
The purpose of this short letter is to clarify which set of pieces of Feynman graphs are resummed in a Loop Vertex Expansion, and to formulate a conjecture on the $\phi^4$ theory in non-integer dimension.
We propose a general multi-class visual recognition model, termed the Classifier Graph, which aims to generalize and integrate ideas from many of today's successful hierarchical recognition approaches. Our graph-based model has the…
Knowledge graphs have recently become the state-of-the-art tool for representing the diverse and complex knowledge of the world. Examples include the proprietary knowledge graphs of companies such as Google, Facebook, IBM, or Microsoft, but…
Graph representations of programs are commonly a central element of machine learning for code research. We introduce an open source Python library python_graphs that applies static analysis to construct graph representations of Python…
In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other…
Graph embedding seeks to build a low-dimensional representation of a graph G. This low-dimensional representation is then used for various downstream tasks. One popular approach is Laplacian Eigenmaps, which constructs a graph embedding…
Closeness is an important measure of network centrality. In this article we will calculate the closeness of graphs, created by using operations on graphs. We will prove a formula for the closeness of shadow graphs. We will calculate the…
The notion of local intrinsic dimensionality (LID) has important theoretical implications and practical applications in the fields of data mining and machine learning. Recent research efforts indicate that LID measures defined for graphs…
In this paper we investigated the possibility to use the magnetic Laplacian to characterize directed graphs (a.k.a. networks). Many interesting results are obtained, including the finding that community structure is related to rotational…
We study two different types of gluing for graphs: interface (obtained by choosing a common subgraph as the gluing component) and bridge gluing (obtained by adding a set of edges to the given subgraphs). We introduce formulae for computing…
In this paper we show how to improve and extend the Integration by Fractional Expansion technique (IBFE) by applying it to certain families of scalar massive Feynman diagrams. The strategy is based on combining this method together with the…
This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…
Scaled relative graphs have been originally introduced in the context of convex optimization and have recently gained attention in the control systems community for the graphical analysis of nonlinear systems. Of particular interest in…