Related papers: New centrality measure: ksi-centrality
We describe and develop three recent novelties in network research which are particularly useful for studying social systems. The first one concerns the discovery of some basic dynamical laws that enable the emergence of the fundamental…
A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and…
We present new values and bounds on the (normalised) closeness centrality $\bar{\mathsf{C}}_C$ of connected graphs and on its product $\bar{l}\bar{\mathsf{C}}_C$ with the mean distance $\bar{l}$ of these graphs. Our main result presents the…
We have defined a new type of clustering scheme preserving the connectivity of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving process. Our new clustering scheme performs much better for correlation length and…
We explore the geometry of complex networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian $(\bb L^+)$. The squared distance of a node $i$ to the origin in this…
Group centrality measures are a generalization of standard centrality, designed to quantify the importance of not just a single node (as is the case with standard measures) but rather that of a group of nodes. Some nodes may have an…
In many fields, the spatial clustering of sampled data points has many consequences. Therefore, several indices have been proposed to assess the level of clustering affecting datasets (e.g. the Morisita index, Ripley's K-function and…
Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify…
Here we present a range-limited approach to centrality measures in both non-weighted and weighted directed complex networks. We introduce an efficient method that generates for every node and every edge its betweenness centrality based on…
We propose the Temporal Walk Centrality, which quantifies the importance of a node by measuring its ability to obtain and distribute information in a temporal network. In contrast to the widely-used betweenness centrality, we assume that…
Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be…
In this paper, we compute normalized Laplacian spectra of central graph of a regular graph, central vertex join and central edge join of two regular graphs. Also, we determine their Kemeny's constant and degree Kirchhoff index.
A new measure to assess the centrality of vertices in an undirected and connected graph is proposed. The proposed measure, L1 centrality, can adequately handle graphs with weights assigned to vertices and edges. The study provides tools for…
In network data analysis, summary statistics of a network can provide us with meaningful insight into the structure of the network. The average clustering coefficient is one of the most popular and widely used network statistics. In this…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
Spectral centrality measures allow to identify influential individuals in social groups, to rank Web pages by their popularity, and even to determine the impact of scientific researches. The centrality score of a node within a network…
The statistical measure of spatial inhomogeneity for n points placed in chi cells each of size kxk is generalized to incorporate finite size objects like black pixels for binary patterns of size LxL. As a function of length scale k, the…
We introduce a statistical quantity, known as the $K$ function, related to the integral of the two--point correlation function. It gives us straightforward information about the scale where clustering dominates and the scale at which…
We study here the clustering of directed social graphs. The clustering coefficient has been introduced to capture the social phenomena that a friend of a friend tends to be my friend. This metric has been widely studied and has shown to be…
This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…