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A common approach to modeling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter…
In recent years extensions of manifold Ricci curvature to discrete combinatorial objects such as graphs and hypergraphs (popularly called as "network shapes"), have found a plethora of applications in a wide spectrum of research areas…
Graph curvature provides geometric priors for Graph Neural Networks (GNNs), enhancing their ability to model complex graph structures, particularly in terms of structural awareness, robustness, and theoretical interpretability. Among…
Many complex networks in the real world have community structures -- groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.…
Network data, commonly used throughout the physical, social, and biological sciences, consist of nodes (individuals) and the edges (interactions) between them. One way to represent network data's complex, high-dimensional structure is to…
The monitoring of large dynamic networks is a major chal- lenge for a wide range of application. The complexity stems from properties of the underlying graphs, in which slight local changes can lead to sizable variations of global prop-…
Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect the local geometry around them. These curvatures have a rich mathematical theory and they have recently found success as a tool to analyze networks…
Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…
Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…
Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
The connection between curvature and topology is a very well-studied theme in the subject of differential geometry. By suitably defining curvature on networks, the study of this theme has been extended into the domain of network analysis as…
A wide range of complex systems can be modeled as networks with corresponding constraints on the edges and nodes, which have been extensively studied in recent years. Nowadays, with the progress of information technology, systems that…
As two main focuses of the study of complex networks, the community structure and the dynamics on networks have both attracted much attention in various scientific fields. However, it is still an open question how the community structure is…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes…
Network embeddings learn to represent nodes as low-dimensional vectors to preserve the proximity between nodes and communities of the network for network analysis. The temporal edges (e.g., relationships, contacts, and emails) in dynamic…
We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…