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We address the question of finding the community structure of a complex network. In an earlier effort [H. Zhou, {\em Phys. Rev. E} (2003)], the concept of network random walking is introduced and a distance measure defined. Here we…
A vision system that can assess its own performance and take appropriate actions online to maximize its effectiveness would be a step towards achieving the long-cherished goal of imitating humans. This paper proposes a method for performing…
Let \( G \) be a finite simple undirected graph. Four graph parameters related to network monitoring are the \emph{geodetic set}, \emph{edge geodetic set}, \emph{strong edge geodetic set}, and \emph{monitoring edge geodetic set}, with…
Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to…
Inhomogeneity in networks can be detected by the analysis of the correlation of the total degree of nearest neighbors. This is illustrated by two models. The first one is a random multi-partitions network that the Aboav Weaire law, which…
The network data has attracted considerable attention in modern statistics. In research on complex network data, one key issue is finding its underlying connection structure given a network sample. The methods that have been proposed in…
Similarity search is a fundamental task for exploiting information in various applications dealing with graph data, such as citation networks or knowledge graphs. While this task has been intensively approached from heuristics to graph…
In image classification, a lot of development has happened in detecting out-of-distribution (OoD) data. However, most OoD detection methods are evaluated on a standard set of datasets, arbitrarily different from training data. There is no…
Graph Neural Networks (GNNs) have improved unsupervised community detection of clustered nodes due to their ability to encode the dual dimensionality of the connectivity and feature information spaces of graphs. Identifying the latent…
The widespread relevance of increasingly complex networks requires methods to extract meaningful coarse-grained representations of such systems. For undirected graphs, standard community detection methods use criteria largely based on…
Highlighting similarities and differences between networks is an informative task in investigating many biological processes. Typical examples are detecting differences between an inferred network and the corresponding gold standard, or…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Many community detection algorithms require the introduction of a measure on the set of nodes. Previously, a lot of efforts have been made to find the top-performing measures. In most cases, experiments were conducted on several datasets or…
Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on…
Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have…
SpectralNet is a graph clustering method that uses neural network to find an embedding that separates the data. So far it was only used with $k$-nn graphs, which are usually constructed using a distance metric (e.g., Euclidean distance).…
Deviations from the average can provide valuable insights about the organization of natural systems. This article extends this important principle to the more systematic identification and analysis of singular local connectivity patterns in…
We present path2vec, a new approach for learning graph embeddings that relies on structural measures of pairwise node similarities. The model learns representations for nodes in a dense space that approximate a given user-defined graph…
Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches,…