相关论文: Graph Information Ratio

A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. The instances of the Weighted Maximum H-Colourable Subgraph problem (MAX H-COL) are edge-weighted graphs G and the objective is to find…

In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…

A growing interest in complex networks theory results in an ongoing demand for new analytical tools. We propose a novel measure based on information theory that provides a new perspective for a better understanding of networked systems:…

In this paper we consider the communication problem that involves transmission of correlated sources over broadcast channels. We consider a graph-based framework for this information transmission problem. The system involves a source coding…

Homophily, the tendency of similar nodes to connect, is a fundamental phenomenon in network science and a critical factor in the performance of graph neural networks (GNNs). While existing studies primarily explore homophily in homogeneous…

Multiplex graphs, characterised by their layered structure, exhibit informative interdependencies within layers that are crucial for understanding complex network dynamics. Quantifying the interaction and shared information among these…

Comparing the top $k$ elements between two or more ranked results is a common task in many contexts and settings. A few measures have been proposed to compare top $k$ lists with attractive mathematical properties, but they face a number of…

Infographics are complex graphic designs integrating text, images, charts and sketches. Despite the increasing popularity of infographics and the rapid growth of online design portfolios, little research investigates how we can take…

The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. In this paper we provide an upper bound of the Harary index in terms of the vertex or edge connectivity of a graph. We…

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very…

Graph representation learning (a.k.a. network embedding) is a significant topic of network analysis, due to its effectiveness to support various graph inference tasks. In this paper, we study the representation learning with multiple…

Feature extraction and description is an important topic of computer vision, as it is the starting point of a number of tasks such as image reconstruction, stitching, registration, and recognition among many others. In this paper, two new…

Let $H$ be a graph on $h$ vertices. The number of induced copies of $H$ in a graph $G$ is denoted by $i_H(G)$. Let $i_H(n)$ denote the maximum of $i_H(G)$ taken over all graphs $G$ with $n$ vertices. Let $f(n,h) = \Pi_{i}^h a_i$ where…

While uncertainty estimation for graphs recently gained traction, most methods rely on homophily and deteriorate in heterophilic settings. We address this by analyzing message passing neural networks from an information-theoretic…

The richness in the content of various information networks such as social networks and communication networks provides the unprecedented potential for learning high-quality expressive representations without external supervision. This…

We define the information threshold as the point of maximum curvature in the prior vs. posterior Bayesian curve, both of which are described as a function of the true positive and negative rates of the classification system in question. The…

Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…

Graph learning on molecules makes use of information from both the molecular structure and the features attached to that structure. Much work has been conducted on biasing either towards structure or features, with the aim that bias…

A new conceptual foundation for the notion of "information" is proposed, based on the concept of a "distinction graph": a graph in which two nodes are connected iff they cannot be distinguished by a particular observer. The "graphtropy" of…

In the $(G,H)$-isomorphism game, a verifier interacts with two non-communicating players (called provers) by privately sending each of them a random vertex from either $G$ or $H$, whose aim is to convince the verifier that two graphs $G$…