Related papers: Entropy of Spatial Network Ensembles
The susceptible--infected--susceptible (SIS) epidemic process on complex networks can show metastability, resembling an endemic equilibrium. In a general setting, the metastable state may involve a large portion of the network, or it can be…
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…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
An information theoretic approach inspired by quantum statistical mechanics was recently proposed as a means to optimize network models and to assess their likelihood against synthetic and real-world networks. Importantly, this method does…
Transport processes on spatial networks are representative of a broad class of real world systems which, rather than being independent, are typically interdependent. We propose a measure of utility to capture key features that arise when…
In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation,…
We quantify a social organization's potentiality, that is its ability to attain different configurations. The organization is represented as a network in which nodes correspond to individuals and (multi-)edges to their multiple…
Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks…
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many…
Statistical ensembles of networks, i.e., probability spaces of all networks that are consistent with given aggregate statistics, have become instrumental in the analysis of complex networks. Their numerical and analytical study provides the…
The analysis of spatial point patterns that occur in the network domain have recently gained much attraction and various intensity functions and measures have been proposed. However, the linkage of spatial network statistics to regression…
We use the concept of the network communicability (Phys. Rev. E 77 (2008) 036111) to define communities in a complex network. The communities are defined as the cliques of a communicability graph, which has the same set of nodes as the…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
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 consider that a network is an observation, and a collection of observed networks forms a sample. In this setting, we provide methods to test whether all observations in a network sample are drawn from a specified model. We achieve this…
The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in…
We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix $\c$, and the relevant statistical ensembles are defined in terms of a partition function $Z=\sum_{\c} \exp {[}-\beta \H(\c)…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated…
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…