Related papers: New centrality measure: ksi-centrality
Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to…
Evaluating the importance of a network node is a crucial task in network science and graph data mining. H-index is a popular centrality measure for this task, however, there is still a lack of its interpretation from a rigorous statistical…
Two concepts of centrality have been defined in complex networks. The first considers the centrality of a node and many different metrics for it has been defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality, etc). The…
We study fair clustering problems as proposed by Chierichetti et al. (NIPS 2017). Here, points have a sensitive attribute and all clusters in the solution are required to be balanced with respect to it (to counteract any form of…
Typing Yesterday into the search-bar of your browser provides a long list of websites with, in top places, a link to a video by The Beatles. The order your browser shows its search results is a notable example of the use of network…
Core-satellite graphs (sometimes referred to as generalized friendship graphs) are an interesting class of graphs that generalize many well known types of graphs. In this paper we show that two popular clustering measures, the average…
Given the increasing popularity of algorithms for overlapping clustering, in particular in social network analysis, quantitative measures are needed to measure the accuracy of a method. Given a set of true clusters, and the set of clusters…
Nodes in real-world networks are usually organized in local modules. These groups, called communities, are intuitively defined as sub-graphs with a larger density of internal connections than of external links. In this work, we introduce a…
Community detection can be considered as a variant of cluster analysis applied to complex networks. For this reason, all existing studies have been using tools derived from this field when evaluating community detection algorithms. However,…
Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a…
Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this…
This paper introduces the notion of co-modularity, to co-cluster observations of bipartite networks into co-communities. The task of co-clustering is to group together nodes of one type with nodes of another type, according to the…
Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper…
The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. Despite some breakthrough works in the mathematical understanding…
The centrality of a node within a network, however it is measured, is a vital proxy for the importance or influence of that node, and the differences in node centrality generate hierarchies and inequalities. If the network is evolving in…
Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…
Many real world systems can be expressed as complex networks of interconnected nodes. It is frequently important to be able to quantify the relative importance of the various nodes in the network, a task accomplished by defining some…
To measure node importance, network scientists employ centrality scores that typically take a microscopic or macroscopic perspective, relying on node features or global network structure. However, traditional centrality measures such as…
Identifying key nodes is crucial for accelerating or impeding dynamic spreading in a network. Community-aware centrality measures tackle this problem by exploiting the community structure of a network. Although there is a growing trend to…
We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is…