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Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices,…
Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…
This paper proposes a logistic undirected network formation model which allows for assortative matching on observed individual characteristics and the presence of edge-wise fixed effects. We model the coefficients of observed…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
Group or cluster structure on explanatory variables in machine learning problems is a very general phenomenon, which has attracted broad interest from practitioners and theoreticians alike. In this work we contribute an approach to learning…
Constrained clustering has been well-studied in the unsupervised learning society. However, how to encode constraints into community structure detection, within complex networks, remains a challenging problem. In this paper, we propose a…
Especially in lattice structured populations, homogeneous mixing represents an inadequate assumption. Various improvements upon the ordinary pair approximation based on a number of assumptions concerning the higher-order correlations have…
We propose an automatable data-driven methodology for robust nonlinear reduced-order modelling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into few centroids representable for the whole…
Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
A proper abstraction of a large-scale linear consensus network with a dense coupling graph is one whose number of coupling links is proportional to its number of subsystems and its performance is comparable to the original network. Optimal…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…
Graph clustering is essential in graph analysis for revealing structural patterns and node communities. Despite recent advances in self-supervised contrastive learning that have improved clustering via structural and attribute signals,…
Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…
The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of…
Performing multiple experiments is common when learning internal mechanisms of complex systems. These experiments can include perturbations to parameters or external disturbances. A challenging problem is to efficiently incorporate all…
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…
In this paper a simple but efficient real-time detecting algorithm is proposed for tracking community structure of dynamic networks. Community structure is intuitively characterized as divisions of network nodes into subgroups, within which…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…