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This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph…

Community detection has arisen as one of the most relevant topics in the field of graph data mining due to its importance in many fields such as biology, social networks or network traffic analysis. The metrics proposed to shape communities…

Geometric graphs form an important family of hidden structures behind data. In this paper, we develop an efficient and robust algorithm to infer a graph skeleton of a high-dimensional point cloud dataset (PCD). Previously, there has been…

We propose a complexity measure which addresses the functional flexibility of networks. It is conjectured that the functional flexibility is reflected in the topological diversity of the assigned graphs, resulting from a resolution of their…

Persistent homology has been studied to better understand the structural properties and topology features of weighted networks. It can reveal hidden layers of information about the higher-order structures formed by non-pairwise interactions…

Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction of large volumes of data embedded in high dimensional…

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…

The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been…

Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such…

We show that the community structure of a network can be used as a coarse version of its embedding in a hidden space with hyperbolic geometry. The finding emerges from a systematic analysis of several real-world and synthetic networks. We…

Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…

Real bipartite networks combine degree-constrained random mixing with structured, locality-like rules. We introduce a statistical filter that benchmarks node-level bipartite clustering against degree-preserving randomizations to classify…

Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…

In complex, high dimensional and unstructured data it is often difficult to extract meaningful patterns. This is especially the case when dealing with textual data. Recent studies in machine learning, information theory and network science…

For decades, complex networks, such as social networks, biological networks, chemical networks, technological networks, have been used to study the evolution and dynamics of different kinds of complex systems. These complex systems can be…

Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…

Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…

Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate…

Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of…