Related papers: Implementing Brouwer's database of strongly regula…
In 2002, D. Fon-Der-Flaass constructed a prolific family of strongly regular graphs. In this paper, we prove that for infinitely many natural numbers $n$, this family contains $n^{\Omega(n^{2/3})}$ strongly regular $n$-vertex graphs $X$…
With the ubiquity of large-scale graph data in a variety of application domains, querying them effectively is a challenge. In particular, reachability queries are becoming increasingly important, especially for containment, subsumption, and…
A Neumaier graph is a non-complete edge-regular graph containing a regular clique. A Neumaier graph that is not strongly regular is called a strictly Neumaier graph. In this work we present a new construction of strictly Neumaier graphs,…
The feasibility conditions obtained in a previous report are refined, and used to determine several infinite families of feasible parameters for strongly regular graphs with no triangles. The methods are also used to improve the lower bound…
We show that for a sequence of random graphs Brouwer's conjecture holds true with probability tending to one as the number of vertices tends to infinity. Surprisingly, it was found that a similar statement holds true for weighted graphs…
This paper proposes a family of permutation-invariant graph embeddings, generalizing the Skew Spectrum of graphs of Kondor & Borgwardt (2008). Grounded in group theory and harmonic analysis, our method introduces a new class of graph…
In this paper we analyze the practical implications of Szemer\'edi's regularity lemma in the preservation of metric information contained in large graphs. To this end, we present a heuristic algorithm to find regular partitions. Our…
Graph databases have emerged as the fundamental technology underpinning trendy application domains where traditional databases are not well-equipped to handle complex graph data. However, current graph databases support basic graph…
We present ABRA, a suite of algorithms that compute and maintain probabilistically-guaranteed, high-quality, approximations of the betweenness centrality of all nodes (or edges) on both static and fully dynamic graphs. Our algorithms rely…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
In order to evaluate, compare, and tune graph algorithms, experiments on well designed benchmark sets have to be performed. Together with the goal of reproducibility of experimental results, this creates a demand for a public archive to…
We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
Advanced Persistent Threats (APTs) are a main impendence in cyber security of computer networks. In 2015, a successful breach remains undetected 146 days on average, reported by [Fi16].With our work we demonstrate a feasible and fast way to…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
The Conway-99 problem questions the existence of a strongly regular graph with 99 vertices and specific parameters. A \textit{strongly} regular graph is a regular graph that exhibits two additional properties: vertices must share a fixed…
In this paper, we give a complete description of strongly regular graphs with parameters ((n^2+3n-1)^2,n^2(n+3),1,n(n+1)). All possible such graphs are: the lattice graph $L_{3,3}$ with parameters (9,4,1,2), the Brouwer-Haemers graph with…
In recent years, researchers proposed several algorithms that compute metric quantities of real-world complex networks, and that are very efficient in practice, although there is no worst-case guarantee. In this work, we propose an…
The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical…
The paper constructs an infinite sequence of strongly regular directed graphs. The construction is based on representing adjacency matrices as block matrices composed of circulant blocks, together with the use of a compactification…