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Weighted evolving networks: coupling topology and weights dynamics This letter examines a new model of network growth where both the edge and node weights can vary dynamically as the network evolves. It is an interesting extension of models like that of Barabasi and Albert where the structure changes but the characteristics of the nodes and edges, once added, are fixed. The model uses the vertex's strength (the sum of the edge weights radiating out from a vertex). At each time step, a new vertex is added and attached to m other vertexes where the probability of attachment is proportional to the existing vertex's strength. Then the pre-existing edge weights are altered via a multiplier delta applied to the existing weight proportional to the vertex's strength. If the multiplier is greater than one, then all the edges get stronger; if less than one, then they get weaker. More complex models can be had if the multiplier itself is allowed to vary with time or the local environment. The authors go on to show that this model leads to the usual power law dynamics with exponents in the usual ranges where the exponent can be derived from the value of the multiplier. It's a nice little piece: a good idea developed quickly with interesting results. Aside from wishing I'd written it, what more could I ask for? <smile> |
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