Related papers: An entropy-based, scale-dependent centrality
The participation coefficient is a widely used metric of the diversity of a node's connections with respect to a modular partition of a network. An information-theoretic formulation of this concept of connection diversity, referred to here…
We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated…
Transfer entropy is an established method for quantifying directed statistical dependencies in neuroimaging and complex systems datasets. The pairwise (or bivariate) transfer entropy from a source to a target node in a network does not…
In this paper, we present a new multi-scale information content calculation method based on Shannon information (and Shannon entropy). The original method described by Claude E. Shannon and based on the logarithm of the probability of…
We consider a system $x(t)=(x_{1}(t),...,x_{N}(t))$ consisting of $N$ Brownian particles with synchronizing interaction between them occurring at random time moments $\{\tau_{n}\}_{n=1}^{\infty}$. Under assumption that the free Brownian…
Centrality measures identify and rank the most influential entities of complex networks. In this paper, we generalize matrix function-based centrality measures, which have been studied extensively for single-layer and temporal networks in…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
Shannon entropy is the most common metric to measure the degree of randomness of time series in many fields, ranging from physics and finance to medicine and biology. Real-world systems may be in general non stationary, with an entropy…
We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions which are of fundamental interest in the theory of critical phenomena and have…
Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…
We consider an isomorphism invariant for measure-preserving systems - types of generalized entropy convergence rates. We show the connections of this invariant with the types of Shannon entropy convergence rates. In the case when they…
Network theory is a useful framework for studying interconnected systems of interacting entities. Many networked systems evolve continuously in time, but most existing methods for the analysis of time-dependent networks rely on discrete or…
In this paper we remark that Shannon entropy can be expressed as a function of the self-information (i.e. the logarithm) and the inverse of the Lambert $W$ function. It means that we consider that Shannon entropy has the trace form: $-k…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…
In this paper, we present a framework for studying the following fundamental question in network analysis: How should one assess the centralities of nodes in an information/influence propagation process over a social network? Our framework…
Temporal networks are such networks where nodes and interactions may appear and disappear at various time scales. With the evidence of ubiquity of temporal networks in our economy, nature and society, it's urgent and significant to focus on…
Complex systems are often inherently non-ergodic and non-Markovian for which Shannon entropy loses its applicability. In particular accelerating, path-dependent, and aging random walks offer an intuitive picture for these non-ergodic and…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
Betweenness centrality lies at the core of both transport and structural vulnerability properties of complex networks, however, it is computationally costly, and its measurement for networks with millions of nodes is near impossible. By…