Related papers: A Complexity Theory for Labeling Schemes
The task of node classification is to infer unknown node labels, given the labels for some of the nodes along with the network structure and other node attributes. Typically, approaches for this task assume homophily, whereby neighboring…
In the List $k$-Coloring problem we are given a graph whose every vertex is equipped with a list, which is a subset of $\{1,\ldots,k\}$. We need to decide if $G$ admits a proper coloring, where every vertex receives a color from its list.…
Image classification is a challenging problem for computer in reality. Large numbers of methods can achieve satisfying performances with sufficient labeled images. However, labeled images are still highly limited for certain image…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered,…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
For each positive integer $n$, we define the divisibility relation graph $D_n$ whose vertex set is the set of divisors of $n$, and in which two vertices are adjacent if one is a divisor of the other. This type of graph is a special case of…
A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals. In this article, we explore various aspects of closed graphs, including the number of closed labelings…
A supervised learning algorithm has access to a distribution of labeled examples, and needs to return a function (hypothesis) that correctly labels the examples. The hypothesis of the learner is taken from some fixed class of functions…
Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for…
Graph Neural Networks (GNNs) have emerged as a powerful tool for semi-supervised node classification tasks. However, recent studies have revealed various biases in GNNs stemming from both node features and graph topology. In this work, we…
It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of…
Node classification and link prediction are widely studied in graph representation learning. While both transductive node classification and link prediction operate over a single input graph, they have so far been studied separately. Node…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
Traditionally, classifying large hierarchical labels with more than 10000 distinct traces can only be achieved with flatten labels. Although flatten labels is feasible, it misses the hierarchical information in the labels. Hierarchical…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that…