Related papers: Triadic First-Order Logic Queries in Temporal Netw…

In a temporal graph, each edge is available at specific points in time. Such an availability point is often represented by a ''temporal edge'' that can be traversed from its tail only at a specific departure time, for arriving in its head…

We introduce graph motif parameters, a class of graph parameters that depend only on the frequencies of constant-size induced subgraphs. Classical works by Lov\'asz show that many interesting quantities have this form, including, for fixed…

The identification of motifs--subgraphs that appear significantly more often in a particular network than in an ensemble of randomized networks--has become a ubiquitous method for uncovering potentially important subunits within networks…

Network structures are extremely important to the study of political science. Much of the data in its subfields are naturally represented as networks. This includes trade, diplomatic and conflict relationships. The social structure of…

Temporal interaction networks capture the history of activities between entities along a timeline. At each interaction, some quantity of data (money, information, kbytes, etc.) flows from one vertex of the network to another. Flow-based…

Many real-world applications give rise to large heterogeneous networks where nodes and edges can be of any arbitrary type (e.g., user, web page, location). Special cases of such heterogeneous graphs include homogeneous graphs, bipartite,…

Biological and technological networks contain patterns, termed network motifs, which occur far more often than in randomized networks. Network motifs were suggested to be elementary building blocks that carry out key functions in the…

We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our…

Network classification has a variety of applications, such as detecting communities within networks and finding similarities between those representing different aspects of the real world. However, most existing work in this area focus on…

A time series motif intuitively is a short time series that repeats itself approximately the same within a larger time series. Such motifs often represent concealed structures, such as heart beats in an ECG recording, the riff in a pop…

Triangle counting is a fundamental technique in network analysis, that has received much attention in various input models. The vast majority of triangle counting algorithms are targeted to static graphs. Yet, many real-world graphs are…

Counting small subgraphs, referred to as motifs, in large graphs is a fundamental task in graph analysis, extensively studied across various contexts and computational models. In the sublinear-time regime, the relaxed problem of approximate…

The analysis of small recurrent substructures, so called network motifs, has become a standard tool of complex network science to unveil the design principles underlying the structure of empirical networks. In many natural systems network…

We consider the problem of sampling and approximately counting an arbitrary given motif $H$ in a graph $G$, where access to $G$ is given via queries: degree, neighbor, and pair, as well as uniform edge sample queries. Previous algorithms…

A graph class $\mathscr{C}$ is called monadically stable if one cannot interpret, in first-order logic, arbitrary large linear orders in colored graphs from $\mathscr{C}$. We prove that the model checking problem for first-order logic is…

Physical and functional constraints on biological networks lead to complex topological patterns across multiple scales in their organization. A particular type of higher-order network feature that has received considerable interest is…

We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…

Complex networks are everywhere. They appear for example in the form of biological networks, social networks, or computer networks and have been studied extensively. Efficient algorithms to solve problems on complex networks play a central…

The structure of the network can be described by motifs, which are subgraphs that often repeat themselves. In order to understand the structure of network motifs, it is of great importance to study subgraphs from the perspective of…

We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use of quantum approximate counting, and all of…