Related papers: New centrality measure: ksi-centrality
Fuzzy K-Means clustering is a critical technique in unsupervised data analysis. Unlike traditional hard clustering algorithms such as K-Means, it allows data points to belong to multiple clusters with varying degrees of membership,…
Understanding the importance of links in transmitting information in a network can provide ways to hinder or postpone ongoing dynamical phenomena like the spreading of epidemic or the diffusion of information. In this work, we propose a new…
A novel method for correlation analysis using scale-dependent Renyi entropies is described. The method involves calculating the entropy of a data distribution as an explicit function of the scale of a d-dimensional partition of d-cubes,…
Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A…
Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected…
This paper proposes a new measure of node centrality in social networks, the Harmonic Influence Centrality, which emerges naturally in the study of social influence over networks. Using an intuitive analogy between social and electrical…
The global clustering coefficient serves as a powerful metric for the structural analysis and comparison of complex networks. Random geometric graphs offer a realistic framework for representing the spatial constraints and geometry often…
Proportional fairness criteria inspired by democratic ideals of proportional representation have received growing attention in the clustering literature. Prior work has investigated them in two separate paradigms. Chen et al. [ICML 2019]…
Motivated by the success of a k-clique percolation method for the identification of overlapping communities in large real networks, here we study the k-clique percolation problem in the Erdos-Renyi graph. When the probability p of two nodes…
The well-known graph-based clustering methods, including spectral clustering, symmetric non-negative matrix factorization, and doubly stochastic normalization, can be viewed as relaxations of the kernel $k$-means approach. However, we posit…
Given a directed network $ G $, we are interested in studying the qualitative features of $ G $ which govern how perturbations propagate across $ G $. Various classical centrality measures have been already developed and proven useful to…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a…
The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central…
The study of social networks is a burgeoning research area. However, most existing work deals with networks that simply encode whether relationships exist or not. In contrast, relationships in signed networks can be positive ("like",…
The evaluation of G-Wishart normalising constants is a core component for Bayesian analyses for Gaussian graphical models, but remains a computationally intensive task in general. Based on empirical evidence, Roverato [Scandinavian Journal…
There is no, nor will there ever be, single best clustering algorithm. Nevertheless, we would still like to be able to distinguish between methods that work well on certain task types and those that systematically underperform. Clustering…
In this article we have shown that the distributions of ksi satisfy an exponential law for real networks while the distributions of ksi for random networks are bell-shaped and closer to the normal distribution. The ksi distributions for…
We incorporate group fairness into the algorithmic centroid clustering problem, where $k$ centers are to be located to serve $n$ agents distributed in a metric space. We refine the notion of proportional fairness proposed in [Chen et al.,…
We show that prominent centrality measures in network analysis are all based on additively separable and linear treatments of statistics that capture a node's position in the network. This enables us to provide a taxonomy of centrality…