Petter Minnhagen

Networks and cities: an information perspective.

Traffic is constrained by the information involved in locating the receiver and the physical distance between sender and receiver. We here focus on the former, and investigate traffic in the perspective of information handling. We replot the road map of cities in terms of the information needed to locate specific addresses and create information city networks with roads mapped to nodes and intersections to links between nodes. These networks have the broad degree distribution found in many other complex networks. The mapping to an information city network makes it possible to quantify the information associated with locating specific addresses.

Hierarchy measures in complex networks.

Using each nodes degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally hierarchical. Comparison with these extremal cases as well as with random scale-free networks allows us to better understand hierarchical versus modular features in several real-life complex networks. For random scale-free topologies the extent of topological hierarchy is shown to smoothly decline with gamma, the exponent of a degree distribution, reaching its highest possible value for gamma</=2 and quickly approaching zero for gamma>3.

Zipf's law unzipped

Why does Zipfs law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous ra ...

XY model in small-world networks

The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the rewiring probability, suggesting a finite-temperature transition for any nonzero rewiring probability. Nature of the phase transition is discussed in comparison with the globally coupled XY model.

Self organized scale-free networks from merging and regeneration

Abstract.We propose that the ubiquitous scale free nature of many real world networks may emerge from a steady state process where nodes are created and merged randomly. The merging may be viewed as an optimization of efficiency by minimizing redundancy.

Simple estimates for vortex fluctuations in connection with high-Tc superconductors

Abstract A description, in terms of two-dimensional vortex fluctuations, of the resistive tail for the resistance parallel to the CuO planes in the case of high- T c superconductors is tested by some simple estimates. This leads to some further suggestions for a consistent description in terms of vortex fluctuations.

Searchability of networks

We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively difficult to search, and thus that the abundance of scale-free networks in nature and society may reflect an attempt to protect local areas in a highly interconnected network from nonrelated communication. In fact, starting from a random node, real-world networks with higher order organization like modular or hierarchical structure are even more difficult to navigate than random scale-free networks. The searchability at the node level opens the possibility for a generalized hierarchy measure that captures both the hierarchy in the usual terms of trees as in military structures, and the intrinsic hierarchical nature of topological hierarchies for scale-free networks as in the Internet.

The meta book and size-dependent properties of written language

Evidence is given for a systematic text-length dependence of the power-law index

Synchronization in interdependent networks

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Vortex Fluctuations, Negative Hall Effect, and Thermally Activated Resistivity in Layered and Thin-Film Superconductors in an External Magnetic Field

of a single book. The estimated