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- Ala Trusina, Sergei Maslov, Petter Minnhagen, Kim Sneppen
- Physical review letters
- 2004

Using each node's 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… (More)

- B J Kim, H Hong, P Holme, G S Jeon, P Minnhagen, M Y Choi
- Physical review. E, Statistical, nonlinear, and…
- 2001

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… (More)

- Seung Ki Baek, Sebastian Bernhardsson, Petter Minnhagen
- ArXiv
- 2010

Why does Zipf's 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 random group division: the elements can be citizens of a country and the groups family names, or the elements can be all the words making up a novel and the groups… (More)

- Petter Holme, Ala Trusina, Beom Jun Kim, Petter Minnhagen
- Physical review. E, Statistical, nonlinear, and…
- 2003

We study Nowak and May's spatial prisoners' dilemma game driven by mutations (random choices of suboptimal strategies) on empirical social networks. The time evolution of the cooperation level is highly complex containing spikes and steps between quasistable levels. A statistical characterization of the quasistable states and a study of the mechanisms… (More)

- Petter Minnhagen, Sebastian Bernhardsson
- PloS one
- 2008

It is suggested that the degree distribution for networks of the cell-metabolism for simple organisms reflects a ubiquitous randomness. This implies that natural selection has exerted no or very little pressure on the network degree distribution during evolution. The corresponding random network, here termed the blind watchmaker network has a power-law… (More)

The gain of a player is the sum of the gain over his/her ties A CC encounter gives both players unity gain A D-D encounter gives both players zero gain A D-C encounter gives the cooperator zero gain and the defector the gain b, 1 < b < 2 * * * * * We use synchronous updating, i.e. loop over: 1. Calculation of individual gain. 2. Choice of Players follows… (More)

Evidence is given for a systematic text-length dependence of the power-law index γ of a single book. The estimated γ values are consistent with a monotonic decrease from 2 to 1 with increasing length of a text. A direct connection to an extended Heap's law is explored. The infinite book limit is, as a consequence, proposed to be given by γ = 1 instead of… (More)

- Sebastian Bernhardsson, Seung Ki Baek, Petter Minnhagen
- ArXiv
- 2011

A " monkey book " is a book consisting of a random distribution of letters and blanks, where a group of letters surrounded by two blanks is defined as a word. We compare the statistics of the word distribution for a monkey book with the corresponding distribution for the general class of random books, where the latter are books for which the words are… (More)

- Jaegon Um, Petter Minnhagen, Beom Jun Kim
- Chaos
- 2011

We explore the synchronization behavior in interdependent systems, where the one-dimensional (1D) network (the intranetwork coupling strength J(I)) is ferromagnetically intercoupled (the strength J) to the Watts-Strogatz (WS) small-world network (the intranetwork coupling strength J(II)). In the absence of the internetwork coupling (J=0), the former network… (More)

It is shown that a real novel shares many characteristic features with a null model in which the words are randomly distributed throughout the text. Such a common feature is a certain translational invariance of the text. Another is that the functional form of the word-frequency distribution of a novel depends on the length of the text in the same way as… (More)