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A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
The complex-step derivative approximation is a numerical differentiation technique that can achieve analytical accuracy, to machine precision, with a single function evaluation. In this letter, the complex-step derivative approximation is…
Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…
The graph isomorphism problem is a main problem which has numerous applications in different fields. Thus, finding an efficient and easy to implement method to discriminate non-isomorphic graphs is valuable. In this paper, a new method is…
Graph sampling allows mining a small representative subgraph from a big graph. Sampling algorithms deploy different strategies to replicate the properties of a given graph in the sampled graph. In this study, we provide a comprehensive…
Graph randomization techniques play a crucial role in network analysis, allowing researchers to assess the statistical significance of observed network properties and distinguish meaningful patterns from random fluctuations. In this survey…
Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the…
Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the…
With the advancement of generative models, the assessment of generated images becomes more and more important. Previous methods measure distances between features of reference and generated images from trained vision models. In this paper,…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method,…
Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…
We consider an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. two histograms are drawn from the same distribution). The…
In a variety of applications, one desires to detect groups of anomalous data samples, with a group potentially manifesting its atypicality (relative to a reference model) on a low-dimensional subset of the full measured set of features.…
We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…
The following question is due to Chatterjee and Varadhan (2011). Fix $0<p<r<1$ and take $G\sim G(n,p)$, the Erd\H{o}s-R\'enyi random graph with edge density $p$, conditioned to have at least as many triangles as the typical $G(n,r)$. Is $G$…
This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…
Recently, a phase transition has been discovered in the network community detection problem below which no algorithm can tell which nodes belong to which communities with success any better than a random guess. This result has, however, so…
The past decade highlighted the usefulness of social network simulations that run on k-regular, n-size, connected graphs. These can be seen as small-scale models of human social networks of large societies. By narrowing down onto k-regular…
Graph sampling via crawling has become increasingly popular and important in the study of measuring various characteristics of large scale complex networks. While powerful, it is known to be challenging when the graph is loosely connected…