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We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of subgraphs with no more than k links are a sufficient statistics for the exponential families of graphs with interactions between at most k links. In this framework we investigate the dependencies between several observables commonly used to quantify structure in networks, such as the degree distribution, cluster and assortativity coefficients.
The success of deep learning has revealed the application potential of neural networks across the sciences and opened up fundamental theoretical problems. In particular, the fact that learning algorithms based on simple variants of gradient methods a
Networks with fat-tailed degree distributions are omnipresent across many scientific disciplines. Such systems are characterized by so-called hubs, specific nodes with high numbers of connections to other nodes. By this property, they are expected to
We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different value of correlation among their entries. Spectra of random netwo
Amorphous materials are coming within reach of realistic computer simulations, but new approaches are needed to fully understand their intricate atomic structures. Here, we show how machine-learning (ML)-based techniques can give new, quantitative ch
It has been shown that the communities of complex networks often overlap with each other. However, there is no effective method to quantify the overlapping community structure. In this paper, we propose a metric to address this problem. Instead of as