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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)
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)
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)
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)
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)
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)
To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are the key to understanding a complex structure. However, specific features may sometimes be neutral and uncorrelated with any system-specific purpose,(More)