Related papers: Discrimination of Graph Isomorphism Classes by Con…
Spectral graph theory is well known and widely used in computer vision. In this paper, we analyze image segmentation algorithms that are based on spectral graph theory, e.g., normalized cut, and show that there is a natural connection…
We give a quasipolynomial time algorithm for the graph matching problem (also known as noisy or robust graph isomorphism) on correlated random graphs. Specifically, for every $\gamma>0$, we give a $n^{O(\log n)}$ time algorithm that given a…
Graph neural network (GNN) is a popular tool to learn the lower-dimensional representation of a graph. It facilitates the applicability of machine learning tasks on graphs by incorporating domain-specific features. There are various options…
In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
This paper considers the graph signal processing problem of anomaly detection in time series of graphs. We examine two related, complementary inference tasks: the detection of anomalous graphs within a time series, and the detection of…
We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph $H$ as a minor can be solved by an algorithm working in time $f(H)\cdot n^{O(1)}$, where $f$ is some function. In other words, we show that these problems…
Classical graph matching aims to find a node correspondence between two unlabeled graphs of known topologies. This problem has a wide range of applications, from matching identities in social networks to identifying similar biological…
Interval and proper interval graphs are very well-known graph classes, for which there is a wide literature. As a consequence, some generalizations of interval graphs have been proposed, in which graphs in general are expressed in terms of…
Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Vertex splitting is a graph modification operation in which a vertex is replaced by multiple vertices such that the union of their neighborhoods equals the neighborhood of the original vertex. We introduce and study vertex splitting as a…
Homomorphism is a key mapping technique between graphs that preserves their structure. Given a graph and a pattern, the subgraph homomorphism problem involves finding a mapping from the pattern to the graph, ensuring that adjacent vertices…
Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal $O(n \log n)$ sampling algorithms on bounded-degree graphs…
Graph classification is a significant problem in many scientific domains. It addresses tasks such as the classification of proteins and chemical compounds into categories according to their functions, or chemical and structural properties.…
Binary classification problems can be naturally modeled as bipartite graphs, where we attempt to classify right nodes based on their left adjacencies. We consider the case of labeled bipartite graphs in which some labels and edges are not…
Exploring small connected and induced subgraph patterns (CIS patterns, or graphlets) has recently attracted considerable attention. Despite recent efforts on computing the number of instances a specific graphlet appears in a large graph…
Graph comparison is fundamentally important for many applications such as the analysis of social networks and biological data and has been a significant research area in the pattern recognition and pattern analysis domains. Nowadays, the…