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In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

Graphs and various graph-like combinatorial structures, such as preorders and hypergraphs, are ubiquitous in programming. This paper focuses on representing graphs in a purely functional programming language like Haskell. There are several…

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…

Endowing brain anatomy, dynamics, and function with a network structure is becoming standard in neuroscience. In its simplest form, a network is a collection of units and relationships between them. The pattern of relations among the units…

Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations,…

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…

Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…

The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…

The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most…

Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…

In the course of the growth of the Internet and due to increasing availability of data, over the last two decades, the field of network science has established itself as an own area of research. With quantitative scientists from computer…

Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant…

Graph-structured data arise naturally in many different application domains. By representing data as graphs, we can capture entities (i.e., nodes) as well as their relationships (i.e., edges) with each other. Many useful insights can be…

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…