Related papers: Implementing Brouwer's database of strongly regula…
In recent years, graph anomaly detection has found extensive applications in various domains such as social, financial, and communication networks. However, anomalies in graph-structured data present unique challenges, including label…
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of…
In general, to draw robust conclusions from a dataset, all the analyzed population must be represented on said dataset. Having a dataset that does not fulfill this condition normally leads to selection bias. Additionally, graphs have been…
We propose a new framework for designing test and query functions for complex structures that vary across a given parameter such as genetic marker position. The operations we are interested in include equality testing, set operations,…
Graph processing is becoming increasingly prevalent across many application domains. In spite of this prevalence, there is little research about how graphs are actually used in practice. We performed an extensive study that consisted of an…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
As graph representations of data emerge in multiple domains, data analysts need to be able to intelligently select among a magnitude of different data graphs based on the effects different graph operators have on them. Exhaustive execution…
Directed Acyclic Graphs (DAGs) are central to uncovering causal structure in complex systems, yet learning a single DAG from data is often challenging: model uncertainty, finite samples, and a combinatorially large search space frequently…
The degree sequence of a graph is the sequence of the degrees of its vertices. If $\pi$ is a degree sequence of a graph $G$, then $G$ is a realization of $\pi$ and $G$ realizes $\pi$. Determining when a sequence of positive integers is…
The degree distribution is one of the most fundamental properties used in the analysis of massive graphs. There is a large literature on graph sampling, where the goal is to estimate properties (especially the degree distribution) of a…
Rigid graph theory is an active area with many open problems, especially regarding embeddings in $\mathbb{R}^d$ or other manifolds, and tight upper bounds on their number for a given number of vertices. Our premise is to relate the number…
With the emergence of social networks, online platforms dedicated to different use cases, and sensor networks, the emergence of large-scale graph community detection has become a steady field of research with real-world applications.…
In this systems paper, we present MillenniumDB: a novel graph database engine that is modular, persistent, and open source. MillenniumDB is based on a graph data model, which we call domain graphs, that provides a simple abstraction upon…
We employ graph database technology to persistently store and retrieve robot domain models.
For certain non linear evolution equations, existence of global in time flows for large data is a fundamental and difficult question. In general, for dispersive and wave equations high regularity of the data does not automatically guarantee…
Graph processing has become an important part of multiple areas of computer science, such as machine learning, computational sciences, medical applications, social network analysis, and many others. Numerous graphs such as web or social…
Highly regular graphs for which not all regularities are explainable by symmetries are fascinating creatures. Some of them like, e.g., the line graph of W.~Kantor's non-classical $\mathrm{GQ}(5^2,5)$, are stumbling stones for existing…
Recent studies have explored graph-based approaches to retrieval-augmented generation, leveraging structured or semi-structured information -- such as entities and their relations extracted from documents -- to enhance retrieval. However,…
Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks…
We report about the results of the application of modern computer algebra tools for construction of directed strongly regular graphs. The suggested techniques are based on the investigation of non-commutative association schemes and Cayley…