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Graph Neural Networks (GNNs) benchmarks often report single point estimates, even when performance differences are small relative to variation across random seeds, train/test splits, and datasets. Confidence intervals, paired comparisons,…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Comparing two geometric graphs embedded in space is important in the field of transportation network analysis. Given street maps of the same city collected from different sources, researchers often need to know how and where they differ.…
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of…
Statistical graph models aim at modeling graphs as random realization among a set of possible graphs. One issue is to evaluate whether or not a graph is likely to have been generated by one particular model. In this paper we introduce the…
The sensitivity of networks regarding the removal of vertices has been studied extensively within the last 15 years. A common approach to measure this sensitivity is (i) removing successively vertices by following a specific removal…
Online social network services provide a platform for human social interactions. Nowadays, many kinds of online interactions generate large-scale social network data. Network analysis helps to mine knowledge and pattern from the…
Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer…
Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance…
Network analysis has become an increasingly prevalent research tool across a vast range of scientific fields. Here, we focus on the particular issue of comparing network statistics, i.e. graph-level measures of network structural features,…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
A wide range of models have been proposed for Graph Generative Models, necessitating effective methods to evaluate their quality. So far, most techniques use either traditional metrics based on subgraph counting, or the representations of…
With the impressive growth of network models in practically every scientific and technological area, we are often faced with the need to compare graphs, i.e., to quantify their (dis)similarity using appropriate metrics. This is necessary,…
Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent…