Journal on Policy and Complex Systems
Search for Community : Rewiring at Random to another Oscillator
In the revision , volatile nodes rewire at random only within the set of volatile nodes in general : a search for community . The idea here is that opinion-vacillating agents recognize others with the same difficulty , breaking ties at random but establishing new ties with other volatile nodes . Here too we can expect a different network structure as a result .
Search for a Leader : Rewiring with Preferential Attachment among Oscillators
In a third form of rewiring , nodes favor other volatile nodes but rewire in preferential attachment to other volatile nodes that have the most connections : a search for a leader .
For 50-node networks initialized with preferential exponents at . 1 intervals between 0 and 3.5 , 10 % of the population was given random opinion changes every 10 ticks of a run , with rewiring in terms of volatility measured after 50 of those changes . Is there a difference in the new networks that form with each of these forms of updating — a difference that shows up in a change of democratic mean ? We performed 1,000 runs with each form of rewiring , taking the average democratic mean of both the initial network and the result after 100,000 ticks .
The results for each form of rewiring are shown in Figure 12 .
Rewiring in response to volatility results in more democratic communication networks with either of two first forms of rewiring : when that rewiring is either to random nodes or to other volatile nodes at random . Within the 100,000 tick limits of our study , the final democratic mean is lower for networks that start with high initial preferential attachment , though the percentage of change for those is even more dramatic .
One of the interesting aspects of this result is that all the networks considered become more democratic with these two forms of rewiring . This includes even those networks that are initially the most “ democratic ” in our sample — those on the lowest end of our preferential exponent scale . As noted in passing , even networks formed initially with a preferential exponent of 0 are not purely random . The order of attaching new nodes in sequence , in the manner of Barabási and Albert ( 1999 ), inherently biases degree distributions in favor of the first nodes . With rewiring to either other nodes or other volatile nodes at random one typically gets a network more random than one with preferential attachment 0 — a network even more democratic than those on our initial scale .
The third case , however , is different . Rewiring as a “ search for a leader ,” itself following a pattern of preferential attachment among volatile nodes , results in a more democratic network only when the initial network had a preferential attachment of greater than 1.1 . For networks that are initially more democratic than that , volatility rewir-
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