Related papers: Network Geometry
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the…
From interacting cellular components to networks of neurons and neural systems, interconnected units comprise a fundamental organizing principle of the nervous system. Understanding how their patterns of connections and interactions give…
Networks are complex models for underlying data in many application domains. In most instances, raw data is not natively in the form of a network, but derived from sensors, logs, images, or other data. Yet, the impact of the various choices…
In recent years, methods from network science are gaining rapidly interest in economics and finance. A reason for this is that in a globalized world the interconnectedness among economic and financial entities are crucial to understand and…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
The extraordinary computational power of the brain may be related in part to the fact that each of the smaller neural networks that compose it can behave transiently in many different ways, depending on its inputs. Mathematically, input…
Spatially embedded networks are shaped by a combination of purely topological (space-independent) and space-dependent formation rules. While it is quite easy to artificially generate networks where the relative importance of these two…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…
With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks,…
We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are…
Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…
Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport…
Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural…
Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…
Networks represent relationships between entities in many complex systems, spanning from online social interactions to biological cell development and brain connectivity. In many cases, relationships between entities are unambiguously…
Complex systems are made up of many interacting components. Network science provides the tools to analyze and understand these interactions. Community detection is a key technique in network science for uncovering the structures that shape…
Graph neural networks provide a powerful toolkit for embedding real-world graphs into low-dimensional spaces according to specific tasks. Up to now, there have been several surveys on this topic. However, they usually lay emphasis on…