Related papers: Entropy distribution and condensation in random ne…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
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…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…
It is often claimed that the entropy of a network's degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former…
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…
The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…
The entropy of a hierarchical network topology in an ensemble of sparse random networks with "hidden variables" associated to its nodes, is the log-likelihood that a given network topology is present in the chosen ensemble.We obtain a…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
This chapter provides a comprehensive and self-contained discussion of the most recent developments of information theory of networks. Maximum entropy models of networks are the least biased ensembles enforcing a set of constraints and are…
In the paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing susceptibilities of different networks to changes in external fields. In the…
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…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
Precisely quantifying the heterogeneity or disorder of a network system is very important and desired in studies of behavior and function of the network system. Although many degree-based entropies have been proposed to measure the…
Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is…
Entropic measures of complexity are able to quantify the information encoded in complex network structures. Several entropic measures have been proposed in this respect. Here we study the relation between the Shannon entropy and the Von…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
New entropy measures have been recently introduced for the quantification of the complexity of networks. Most of these entropy measures apply to static networks or to dynamical processes defined on static complex networks. In this paper we…