A nonlinear model has been posited for the global analysis of data pertaining to the semantic network of a complex operating system (free and open-source software). While the distribution of links in the dependency network of this system is scale-free for the intermediate nodes, the richest nodes  deviate from this trend, and exhibit a nonlinearity-induced saturation effect. This also distinguishes the two directed networks of incoming and outgoing links from each other. The initial condition for a dynamic model, evolving towards the steady dependency distribution , determines the saturation properties of the mature scale-free network .
A continuum model has been posited for the global analysis of data pertaining to the semantic network of a complex operating system (free and open-source software). While the frequency distributions of links in both the in-directed and out-directed dependency networks of this system follow Zipf's law for the intermediate nodes, the richest nodes , as well as the weakest nodes, deviate from this trend, and exhibit a saturation behaviour arising from the finiteness of semantic possibilities in the network. To preserve uniqueness of operations in the network, the nodes obey an "exclusion principle", with no two nodes being exactly alike in their functionality. The parameters related to finite-size behaviour make a quantitative distinction between the two directed networks of incoming and outgoing links . Dynamic evolution, over two generations of free software releases, shows that the saturation properties of the in-directed and out-directed networks are oppositely affected. For the out-degree distribution, whose top nodes form the foundation of the entire network, the initial condition for a dynamic model, evolving towards a steady scale-free frequency distribution of nodes , determines the finite limit to the number of top nodes that the mature out-directed network can have .
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nonlinear
continuum
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distribution
frequency distributions
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the dependency network
both the in-directed and out-directed dependency networks
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is scale-free
follow Zipf's law
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, as well as the weakest nodes,
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nonlinearity-induced saturation effect. This also distinguishes the two
saturation behaviour arising from the finiteness of semantic possibilities in the network. To preserve uniqueness of operations in the network, the nodes obey an "exclusion principle", with no two nodes being exactly alike in their functionality. The parameters related to finite-size behaviour make a quantitative distinction between the two
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from each other. The
. Dynamic evolution, over two generations of free software releases, shows that the saturation properties of the in-directed and out-directed networks are oppositely affected. For the out-degree distribution, whose top nodes form the foundation of the entire network, the
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the steady dependency distribution
a steady scale-free frequency distribution of nodes
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saturation properties of the mature scale-free network
finite limit to the number of top nodes that the mature out-directed network can have