Related papers: Hidden geometry and dynamics of complex networks: …

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…

Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…

A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that…

Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that…

Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

Localized topological defects inherently possess a multiscale character. While their microstructure configuration depends on the specific physical system, their topological features and mutual interactions can be described on the macroscale…

Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…

Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…

We investigate the ground-state properties of triangular graphene nanoflakes with zigzag edge configurations. The description of zero-dimensional nanostructures requires accurate many-body techniques since the widely used density-functional…

Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding the information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their…

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis,…

Disordered spring networks that are undercoordinated may abruptly rigidify when sufficient strain is applied. Since the deformation in response to applied strain does not change the generic quantifiers of network architecture - the number…

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

Motivated by the idea of using simple macroscopic examples to illustrate the physics of complex systems, we modify a historic experimental setup in which interacting floating magnets spontaneously self-assemble into ordered clusters. By…

Empirical and theoretical works show that the input weights of two-layer neural networks, when initialized with small values, converge towards isolated orientations. This phenomenon, referred to as condensation, indicates that the gradient…

Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…

Deep neural networks employ specialized architectures for vision, sequential and language tasks, yet this proliferation obscures their underlying commonalities. We introduce a unified matrix-order framework that casts convolutional,…

Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy…

The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern the formation and evolution…