Related papers: Graph Pseudometrics from a Topological Point of Vi…

Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a…

Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…

An important tool in analyzing complex social and information networks is s-t simple path counting, which is known to be #P-complete. In this paper, we study efficient s-t simple path counting in directed graphs. For a given pair of…

Symmetry is an important aesthetic criteria in graph drawing and network visualisation. Symmetric graph drawings aim to faithfully represent automorphisms of graphs as geometric symmetries in a drawing. In this paper, we design and…

Studying the topology of so-called real networks, that is networks obtained from sociological or biological data for instance, has become a major field of interest in the last decade. One way to deal with it is to consider that networks are…

In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and…

Many community detection algorithms require the introduction of a measure on the set of nodes. Previously, a lot of efforts have been made to find the top-performing measures. In most cases, experiments were conducted on several datasets or…

Graph drawings are commonly used to visualize relational data. User understanding and performance are linked to the quality of such drawings, which is measured by quality metrics. The tacit knowledge in the graph drawing community about…

We consider a statistical model for the problem of finding subgraphs with specified topology in an otherwise random graph. This task plays an important role in the analysis of social and biological networks. In these types of networks,…

For various purposes and, in particular, in the context of data compression, a graph can be examined at three levels. Its structure can be described as the unlabeled version of the graph; then the labeling of its structure can be added; and…

Graph sampling via crawling has become increasingly popular and important in the study of measuring various characteristics of large scale complex networks. While powerful, it is known to be challenging when the graph is loosely connected…

Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their…

Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…

Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…

Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data…

Characterizing motif (i.e., locally connected subgraph patterns) statistics is important for understanding complex networks such as online social networks and communication networks. Previous work made the strong assumption that the graph…

For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…

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…

We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…