Related papers: A rigorous and efficient approach to finding and q…
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…
Graph drawings are useful tools for exploring the structure and dynamics of data that can be represented by pair-wise relationships among a set of objects. Typical real-world social, biological or technological networks exhibit high…
We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…
Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
This paper presents a framework for the study of convergence when the nodes' dynamics may be both piecewise smooth and/or nonidentical across the network. Specifically, we derive sufficient conditions for global convergence of all node…
The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…
In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…
Symmetries are ubiquitous in real networks and often characterize network features and functions. Here we present a generalization of network symmetry called \emph{latent symmetry}, which is an extension of the standard notion of symmetry.…
We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster. In this model, the group…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
Heterogeneous networks are widely used to model real-world semi-structured data. The key challenge of learning over such networks is the modeling of node similarity under both network structures and contents. To deal with network…
The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein…
Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
In this paper, we investigate community detection in networks in the presence of node covariates. In many instances, covariates and networks individually only give a partial view of the cluster structure. One needs to jointly infer the full…
We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more…
Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here…
Discovering and tracking communities in time-varying networks is an important task in network science, motivated by applications in fields ranging from neuroscience to sociology. In this work, we characterize the celebrated family of…