We suggest a method for embedding scale-free networks, with degree distribution Pk approximately k(-lambda), in regular Euclidean lattices accounting for geographical properties. The embedding is driven by a natural constraint of minimization of the total length of the links in the system. We find that all networks with lambda>2 can be successfully embedded up to a (Euclidean) distance xi which...

1 University of California at Berkeley, Berkeley, CA 94720, USA 2 University of Memphis, Memphis TN 38152, USA 3 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, UK. Research supported in part by NSF grants DMS-0505550, CNS-0721983 and CCF-0728928, and ARO grant W911NF-06-1-0076. 4 Mathematical Institute, University of Oxford, 24–29 St Gile...

A central claim in modern network science is that real-world networks are typically “scale free,” meaning that the fraction of nodes with degree k follows a power law, decaying like k−α, often with 2 < α < 3. However, empirical evidence for this belief derives from a relatively small number of real-world networks. We test the universality of scale-free structure by applying state-of-the-art sta...

We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on scale-free (SF) networks, where the threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent tau. Applying the theory of the multiplicative branching process, we obtain the exponent tau and the dynamic ...

Many real, complex networks have been shown to be scale-free. Scale-free in networks mean that their degree distribution is independent of the network size, have short path lengths and are highly clustered. We identify the qualities of scale-free networks, and discuss the mathematical derivations and numerically simulated outcomes of various deterministic scale-free models. Information Systems ...

Functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites. Analysis of the resulting networks in different tasks shows that (a) the distribution of functional connections, and the probability of finding a link versus distance are both scale-free, (b) the characteristic path length is small and comparable with those of equivalent random ...

We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power-law distribution of degree, linear preferential attachment of new links, and a negative correlation between the age of a node and its link attachment rate. Notably, the degree distribution is conserved even though only the most recently grown part of the...