Related papers: An entropy-based, scale-dependent centrality
We introduce a new measure of interdependence among the components of a random vector along the main diagonal of the vector copula, i.e. along the line $u_{1}=\ldots=u_{J}$, for $\left(u_{1},\ldots,u_{J}\right)\in\left[0,1\right]^{J}$. Our…
Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…
In complex scale-free networks, ranking the individual nodes based upon their importance has useful applications, such as the identification of hubs for epidemic control, or bottlenecks for controlling traffic congestion. However, in most…
Many popular measures used in social network analysis, including centrality, are based on the random walk. The random walk is a model of a stochastic process where a node interacts with one other node at a time. However, the random walk may…
Centrality measures have been defined to quantify the importance of a node in complex networks. The relative importance of a node can be measured using its centrality rank based on the centrality value. In the present work, we predict the…
The analysis of temporal networks heavily depends on the analysis of time-respecting paths. However, before being able to model and analyze the time-respecting paths, we have to infer the timescales at which the temporal edges influence…
We perform the first axiomatic analysis of medial centrality measures. These measures, also called betweenness-like centralities, assess the role of a node in connecting others in the network. We focus on a setting with one target node and…
In this paper we generalize the concept of random networks to describe networks with non trivial features by a statistical mechanics approach. This framework is able to describe ensembles of undirected, directed as well as weighted…
We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive…
In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…
One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…
I consider the effect of a finite sample size on the entropy of a sample of independent events. I propose formula for entropy which satisfies Shannon's axioms, and which reduces to Shannon's entropy when sample size is infinite. I discuss…
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…
We derive a composite centrality measure for general weighted and directed complex networks, based on measure standardisation and invariant statistical inheritance schemes. Different schemes generate different intermediate abstract measures…
Group centrality is an extension of the classical notion of centrality for individuals, to make it applicable to sets of them. We perform a SWOT (strengths, weaknesses, opportunities and threats) analysis of the use of group centrality in…
Entropies based on walks on graphs and on their line-graphs are defined. They are based on the summation over diagonal and off-diagonal elements of the thermal Green's function of a graph also known as the communicability. The walk…
In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
The fractional order generalization of Shannon entropy proposed by Ubriaco has been studied for discrete distributions. In the current paper, we conduct a detailed study of the continuous analogue of this entropy termed as fractional…
Measures of node centrality that describe the importance of a node within a network are crucial for understanding the behavior of social networks and graphs. In this paper, we address the problems of distributed estimation and control of…