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Graph neural networks (GNN) have achieved remarkable success in a wide range of tasks by encoding features combined with topology to create effective representations. However, the fundamental problem of understanding and analyzing how graph…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
Functional brain networks exhibit topological structures that reflect neural organization; however, statistical comparison of these networks is challenging for several reasons. This paper introduces a topologically invariant permutation…
Unravelling the block structure of a network is critical for studying macroscopic features and community-level dynamics. The weighted stochastic block model (WSBM), a variation of the traditional stochastic block model, is designed for…
Network tomography is a crucial problem in network monitoring, where the observable path performance metric values are used to infer the unobserved ones, making it essential for tasks such as route selection, fault diagnosis, and traffic…
In this paper, we consider the problem of recovering a graph that represents the statistical data dependency among nodes for a set of data samples generated by nodes, which provides the basic structure to perform an inference task, such as…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
Community structure is of paramount importance for the understanding of complex networks. Consequently, there is a tremendous effort in order to develop efficient community detection algorithms. Unfortunately, the issue of a fair assessment…
Network theory provides a rich toolbox consisting of methods, measures, and models for studying the structure and dynamics of complex systems found in nature, society, or technology. Recently, it has been pointed out that many real-world…
Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological…
Functional connections in the brain are frequently represented by weighted networks, with nodes representing locations in the brain, and edges representing the strength of connectivity between these locations. One challenge in analyzing…
Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This paper discusses a theoretical…
Recent years have witnessed the remarkable success of applying Graph machine learning (GML) to node/graph classification and link prediction. However, edge classification task that enjoys numerous real-world applications such as social…
Community detection refers to the problem of clustering the nodes of a network into groups. Existing inferential methods for community structure mainly focus on unweighted (binary) networks. Many real-world networks are nonetheless weighted…
We address the problem of inferring the topology of a wireless network using limited observational data. Specifically, we assume that we can detect when a node is transmitting, but no further information regarding the transmission is…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation…
Edge intelligence has arisen as a promising computing paradigm for supporting miscellaneous smart applications that rely on machine learning techniques. While the community has extensively investigated multi-tier edge deployment for…
Functional complex networks have meant a pivotal change in the way we understand complex systems, being the most outstanding one the human brain. These networks have classically been reconstructed using a frequentist approach that, while…
We study the robustness of complex networks subject to edge removal. Several network models and removing strategies are simulated. Rather than the existence of the giant component, we use total connectedness as the criterion of breakdown.…