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Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
We introduce NetworKit, an open-source software package for analyzing the structure of large complex networks. Appropriate algorithmic solutions are required to handle increasingly common large graph data sets containing up to billions of…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
The all-terminal reliability of a graph $G$ is the probability that $G$ remains connected when each edge fails independently with probability $p$. For fixed $n$ and $m$, the uniformly most reliable problem asks which graph with $n$ vertices…
In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…
Rigid graphs have only finitely many realizations. In the recent years significant progress was made in computing the number of such realizations. With this progress it was also possible for the first time to do computations on large sets…
Jord\'an and Tanigawa recently introduced the $d$-dimensional algebraic connectivity $a_d(G)$ of a graph $G$. This is a quantitative measure of the $d$-dimensional rigidity of $G$ which generalizes the well-studied notion of spectral…
We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and,…
We exactly settle the complexity of graph realization, graph rigidity, and graph global rigidity as applied to three types of graphs: "globally noncrossing" graphs, which avoid crossings in all of their configurations; matchstick graphs,…
Graph generative models become increasingly effective for data distribution approximation and data augmentation. While they have aroused public concerns about their malicious misuses or misinformation broadcasts, just as what Deepfake…
We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck^2/\log^* k pairs of parts which are not \epsilon-regular, where c,\epsilon>0 are absolute…
We introduce a notion for hierarchical graph clustering which we call the expander hierarchy and show a fully dynamic algorithm for maintaining such a hierarchy on a graph with $n$ vertices undergoing edge insertions and deletions using…
We present a dynamic data structure representing a graph G, which allows addition and removal of edges from G and can determine the number of appearances of a graph of a bounded size as an induced subgraph of G. The queries are answered in…
Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and…
Big data and the Internet of Things era continue to challenge computational systems. Several technology solutions such as NoSQL databases have been developed to deal with this challenge. In order to generate meaningful results from large…
Graph Anomaly Detection (GAD) has recently become a hot research spot due to its practicability and theoretical value. Since GAD emphasizes the application and the rarity of anomalous samples, enriching the varieties of its datasets is…
Anomaly detection aims to distinguish abnormal instances that deviate significantly from the majority of benign ones. As instances that appear in the real world are naturally connected and can be represented with graphs, graph neural…
In the deeply interconnected world we live in, pieces of information link domains all around us. As graph databases embrace effectively relationships among data and allow processing and querying these connections efficiently, they are…
For supervised learning with tabular data, decision tree ensembles produced via boosting techniques generally dominate real-world applications involving iid training/test sets. However for graph data where the iid assumption is violated due…