Related papers: Graph Information Ratio
The principal ratio of a connected graph $G$, $\gamma(G)$, is the ratio between the largest and smallest coordinates of the principal eigenvector of the adjacency matrix of $G$. Over all connected graphs on $n$ vertices, $\gamma(G)$ ranges…
This paper deals with three graph characteristics related to graph covering named the (vertex, edge, and total, resp.) H-irregularity strength of a graph G admitting H-covering. Those are the minimum values of positive integer k such that G…
For graphs $G$ and $H$, an {\em $H$-colouring} of $G$ (or {\em homomorphism} from $G$ to $H$) is a function from the vertices of $G$ to the vertices of $H$ that preserves adjacency. $H$-colourings generalize such graph theory notions as…
Document coherence describes how much sense text makes in terms of its logical organisation and discourse flow. Even though coherence is a relatively difficult notion to quantify precisely, it can be approximated automatically. This type of…
Perfect secret sharing scheme is a method of distribute a secret information $s$ among participants such that only predefined coalitions, called qualified subsets of the participants can recover the secret, whereas any other coalitions, the…
The independent domination number $i(G)$ of a graph $G$ is the minimum cardinality of a maximal independent set of $G$, also called an $i(G)$-set. The $i$-graph of $G$, denoted $\mathcal{I}(G)$, is the graph whose vertices correspond to the…
The Hall ratio of a graph $G$ is the maximum value of $v(H) / \alpha(H)$ taken over all non-null subgraphs $H$ of $G$. For any graph, the Hall ratio is a lower-bound on its fractional chromatic number. In this note, we present various…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
The concept of the \textit{relative fractional packing number} between two graphs $G$ and $H$, initially introduced in arXiv:2307.06155 [math.CO], serves as an upper bound for the ratio of the zero-error Shannon capacity of these graphs.…
For a positive integer $k$ and a graph $H$ on $k$ vertices, we are interested in the inducibility of $H$, denoted $\mathrm{ind}(H)$, which is defined as the maximum possible probability that choosing $k$ vertices uniformly at random from a…
We estimate the maximum ratio between the $\sigma_t$- and $\sigma$-irregularity for graphs and trees of order $n$, which are respectively bounded by $\Theta(n^{5/2})$ and $n-2$. This answers a question and a conjecture by Filipovski et al.…
In network analysis, a measure of node centrality provides a scale indicating how central a node is within a network. The coreness is a popular notion of centrality that accounts for the maximal smallest degree of a subgraph containing a…
Graph contrastive learning (GCL) emerges as the most representative approach for graph representation learning, which leverages the principle of maximizing mutual information (InfoMax) to learn node representations applied in downstream…
Graph matching pairs corresponding nodes across two or more graphs. The problem is difficult as it is hard to capture the structural similarity across graphs, especially on large graphs. We propose to incorporate high-order information for…
We study the problem of profiling news media on the Web with respect to their factuality of reporting and bias. This is an important but under-studied problem related to disinformation and "fake news" detection, but it addresses the issue…
The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$ labels that is preserved only by a trivial automorphism. The strong product $G\boxtimes…
In this paper, we study an information-theoretic problem of designing a fair representation under a bounded point-wise statistical (demographic) parity constraint. More specifically, an agent uses some useful data (database) $X$ to solve a…
Various graph neural networks (GNNs) have been proposed to solve node classification tasks in machine learning for graph data. GNNs use the structural information of graph data by aggregating the features of neighboring nodes. However, they…
Citation distributions are lognormal. We use 30 lognormally distributed synthetic series of numbers that simulate real series of citations to investigate the consistency of the h index. Using the lognormal cumulative distribution function,…
Graph Neural Networks (GNNs) achieve an impressive performance on structured graphs by recursively updating the representation vector of each node based on its neighbors, during which parameterized transformation matrices should be learned…