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We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…

Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…

Hypergraph clustering is a basic algorithmic primitive for analyzing complex datasets and systems characterized by multiway interactions, such as group email conversations, groups of co-purchased retail products, and co-authorship data.…

Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this…

Disentanglement via mechanism sparsity was introduced recently as a principled approach to extract latent factors without supervision when the causal graph relating them in time is sparse, and/or when actions are observed and affect them…

Can we employ one neural model to efficiently dismantle many complex yet unique networks? This article provides an affirmative answer. Diverse real-world systems can be abstracted as complex networks each consisting of many functional nodes…

In this paper, we establish a method for model order reduction of a certain class of physical network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the…

Local clustering aims at extracting a local structure inside a graph without the necessity of knowing the entire graph structure. As the local structure is usually small in size compared to the entire graph, one can think of it as a…

We introduce network $L$-cloning, a technique for creating ensembles of random networks from any given real-world or artificial network. Each member of the ensemble is an $L$-cloned network constructed from $L$ copies of the original…

In recent years, deep learning has achieved remarkable success in the field of image restoration. However, most convolutional neural network-based methods typically focus on a single scale, neglecting the incorporation of multi-scale…

Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…

We propose an efficient linear-time graph-based divisive cluster analysis approach called Reductive Clustering. The approach tries to reveal the hierarchical structural information through reducing the graph into a more concise one…

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…

We propose a novel model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the…

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…

Optimal percolation concerns the identification of the minimum-cost strategy for the destruction of any extensive connected components in a network. Solutions of such a dismantling problem are important for the design of optimal strategies…

Graph Neural Networks often struggle with long-range information propagation and in the presence of heterophilous neighborhoods. We address both challenges with a unified framework that incorporates a clustering inductive bias into the…

Infomap clustering finds the community structures that minimize the expected description length of a random walk trajectory; algorithms for infomap clustering run fast in practice for large graphs. In this paper we leverage the…

From physics to engineering, biology and social science, natural and artificial systems are characterized by interconnected topologies whose features - e.g., heterogeneous connectivity, mesoscale organization, hierarchy - affect their…

One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…