Related papers: Graph Information Ratio
Given a graph $G$ and a non trivial partition $(V_1,V_2)$ of its vertex-set, the satisfaction of a vertex $v\in V_i$ is the ratio between the size of it's closed neighborhood in $V_i$ and the size of its closed neighborhood in $G$. The…
The principal ratio of a graph is the ratio of the greatest and least entry of its principal eigenvector. Since the principal ratio compares the extreme values of the principal eigenvector it is sensitive to outliers. This can be…
We propose two new spectral measures for graphs and networks which characterize the ratios between the width of the "bulk" part of the spectrum and the spectral gap, as well as the ratio between spectral length and the width of the "bulk"…
A secure storage code maps $K$ source symbols, each of $L_w$ bits, to $N$ coded symbols, each of $L_v$ bits, such that each coded symbol is stored in a node of a graph. Each edge of the graph is either associated with $D$ of the $K$ source…
An independent set $I$ in a graph $G$ is maximal if $I$ is not properly contained in any other independent set of $G$. The study of maximal independent sets (MIS's) in various graphs is well-established, often focusing upon enumeration of…
The total irregularity of a graph $G$ is defined as $\irr_t(G)=1/2 \sum_{u,v \in V(G)}$ $|d_G(u)-d_G(v)|$, where $d_G(u)$ denotes the degree of a vertex $u \in V(G)$. In this paper we give (sharp) upper bounds on the total irregularity of…
Under circumstances of heterophily, where nodes with different labels tend to be connected based on semantic meanings, Graph Neural Networks (GNNs) often exhibit suboptimal performance. Current studies on graph heterophily mainly focus on…
Homophily is a graph property describing the tendency of edges to connect similar nodes; the opposite is called heterophily. It is often believed that heterophilous graphs are challenging for standard message-passing graph neural networks…
Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer…
Adaptive systems must strike a balance between prediction and surprise to thrive in uncertain environments. We propose an information-theoretic balance function, $ f(p) = -(1 - p)\ln(1 - p) + \ln p $, which quantifies the net informational…
Let $G$ be a simple connected undirected graph. The Laplacian spectral ratio of $G$, denoted by $R_L(G)$, is defined as the quotient between the largest and second smallest Laplacian eigenvalues of $G$, which is closely related to the…
Heterogeneous graph representation learning aims to learn low-dimensional vector representations of different types of entities and relations to empower downstream tasks. Existing methods either capture semantic relationships but indirectly…
Unsupervised (or self-supervised) graph representation learning is essential to facilitate various graph data mining tasks when external supervision is unavailable. The challenge is to encode the information about the graph structure and…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
Given a graph $H$, a perfect $H$-factor in a graph $G$ is a collection of vertex-disjoint copies of $H$ spanning $G$. K\"uhn and Osthus showed that the minimum degree threshold for a graph $G$ to contain a perfect $H$-factor is either given…
Information-based complexity (IBC) is a well-defined complexity measure of any object given a description in a language and a classifier that identifies those descriptions with the object. Of course, the exact numerical value will vary…
There is arbitrariness in optimum solutions of graph-theoretic problems that can give rise to unfairness. Incorporating fairness in such problems, however, can be done in multiple ways. For instance, fairness can be defined on an individual…
Let $G$ be a connected graph, the principal ratio of $G$ is the ratio of the maximum and minimum entries of its Perron eigenvector. In 2007, Cioab\v a and Gregory conjectured that among all connected graphs on $n$ vertices, the kite graph…
Information retrieval (IR) systems often leverage query data to suggest relevant items to users. This introduces the possibility of unfairness if the query (i.e., input) and the resulting recommendations unintentionally correlate with…
Provable lower bounds are presented for the information rate I(X; X+S+N) where X is the symbol drawn independently and uniformly from a finite-size alphabet, S is a discrete-valued random variable (RV) and N is a Gaussian RV. It is well…