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Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
The frequency allocation problem that appeared in the design of cellular telephone networks can be regarded as a multicoloring problem on a weighted hexagonal graph, which opened some still interesting mathematical problems. We generalize…
One fundamental problem in temporal graph analysis is to count the occurrences of small connected subgraph patterns (i.e., motifs), which benefits a broad range of real-world applications, such as anomaly detection, structure prediction,…
Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity,…
Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these…
The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…
Network reconstruction is the task of inferring the unseen interactions between elements of a system, based only on their behavior or dynamics. This inverse problem is in general ill-posed, and admits many solutions for the same…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
Starting with an initial random network of oscillators with a heterogeneous frequency distribution, its autonomous synchronization ability can be largely improved by appropriately rewiring the links between the elements. Ensembles of…
In the quest to improve efficiency, interdependence and complexity are becoming defining characteristics of modern complex networks representing engineered and natural systems. Graph theory is a widely used framework for modeling such…
Estimating the frequency of sub-graphs is of importance for many tasks, including sub-graph isomorphism, kernel-based anomaly detection, and network structure analysis. While multiple algorithms were proposed for full enumeration or…
Understanding decisions made by neural networks is key for the deployment of intelligent systems in real world applications. However, the opaque decision making process of these systems is a disadvantage where interpretability is essential.…
Finding hidden layers in complex networks is an important and a non-trivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multi-layer system exist and if so then what is…
A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state energy without an uncontrolled bias. This is achieved by confining signed…
This work addresses the rising demand for novel tools in statistical and machine learning for "graph-valued random variables" by proposing a fast algorithm to compute the sample Frechet mean, which replaces the concept of sample mean for…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
In a diffusion process on a network, how many nodes are expected to be influenced by a set of initial spreaders? This natural problem, often referred to as influence estimation, boils down to computing the marginal probability that a given…