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This paper introduces an efficient quantum computing method for reducing special graphs in the context of the graph coloring problem. The special graphs considered include both symmetric and non-symmetric graphs where the axis passes…
There are many concepts of signed graph coloring which are defined by assigning colors to the vertices of the graphs. These concepts usually differ in the number of self-inverse colors used. We introduce a unifying concept for this kind of…
Graph coarsening reduces the size of a graph while preserving certain properties. Most existing methods preserve either spectral or spatial characteristics. Recent research has shown that preserving topological features helps maintain the…
Computing subgraph frequencies is a fundamental task that lies at the core of several network analysis methodologies, such as network motifs and graphlet-based metrics, which have been widely used to categorize and compare networks from…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to algebraic tool for modeling the structure via nodes and edges…
Graph neural networks have received increased attention over the past years due to their promising ability to handle graph-structured data, which can be found in many real-world problems such as recommended systems and drug synthesis. Most…
Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…
The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with problems of algebra, statistical mechanics and planning.…
Many applications, ranging from natural to social sciences, rely on graphlet analysis for the intuitive and meaningful characterization of networks employing micro-level structures as building blocks. However, it has not been thoroughly…
Graph coloring, a classical and critical NP-hard problem, is the problem of assigning connected nodes as different colors as possible. However, we observe that state-of-the-art GNNs are less successful in the graph coloring problem. We…
Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the…
Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests…
Despite the success of the carefully-annotated benchmarks, the effectiveness of existing graph neural networks (GNNs) can be considerably impaired in practice when the real-world graph data is noisily labeled. Previous explorations in…
Graph contrastive learning (GCL) has recently emerged as a new concept which allows for capitalizing on the strengths of graph neural networks (GNNs) to learn rich representations in a wide variety of applications which involve abundant…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
Network tomography plays a crucial role in network monitoring and management, where network topology serves as the fundamental basis for various tomography tasks including traffic matrix estimation and link performance inference. The…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
Communication networks form the backbone of our society. Topology control algorithms optimize the topology of such communication networks. Due to the importance of communication networks, a topology control algorithm should guarantee…
We address the problem of computing the distribution of induced connected subgraphs, aka \emph{graphlets} or \emph{motifs}, in large graphs. The current state-of-the-art algorithms estimate the motif counts via uniform sampling, by…