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Fig. 5.2. The units forming the simple model are placed on the nodes of a one-dimensional
lattice and establish bi-directional nearest-neighbor connections. With some probability we add
long-range unidirectional connections until there are k e N of such excess links, k e being the average
excess connectivity, and N the number of units. Each unit processes a set of input signals in the
way that it is described in the text. The signal received from one of its neighbors is replaced with
a random value with probability .
a minimal set of ingredients, we can show the relationship between age or disease,
lost of links, noise, and the spectrum of the resulting uctuations.
5.4.1. Topology
Concerning the system's topology of simple signalling model networks, we assume
that the units are placed on the nodes of a one-dimensional lattice and that each
unit is bidirectionally connected to its two nearest neighbors. We then increase the
topological complexity of the system by adding, with probability k e , an incoming
connection to each node [Newman and Watts (1999)] (Fig. 5.2). The basic topology
we considered consists in placing units on a circle with connections to the nearest-
neighbors. This is a very regular, ordered (and articial) network structure. To
consider a more general topology we rst allow for \connection errors," which we
implement through long-range connections to randomly-selected units on the cir-
cle (\short-cuts"). This corresponds to the \small-world" topology proposed by
Watts and Strogatz (1998); Strogatz (2001). Although quite stylized, this topol-
ogy captures some aspects of real-world networks such as (i) the small number
of \degrees-of-separation" between the units and (ii) the local order through the
clustering coecient.
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