In a directed network of agents passing knowledge to each other how fast does information in a node grow with the number of edges incident on it? Linearly or exponentially with the number of edges? If on one hand the knowledge of the node agent seems to grow with the sum of the knowledge shared through the incoming edges, on the other hand each item of information shared through one edge might recombine with each item of other edges incoming information, to form new items of information. For example if agent A tells me that there is a traffic jam near the shopping center and agent B tells me that today morning there are big sales there, I get to acquire a third peace of information from combining what agent A and Agent B told me, which is that the traffic jam is caused by the sales and won't stop until the sails are over. Any ideas on which model better suits reality? Sorry if this sounds as a rather naïve question, but since it is related, but not central to my research, I did not get to do a literature search on it.
Stephen Strogatz has a few well-known papers on the "small-world" theory of graphs. A usual approach to the problem is to first define a generative model to the graph/network and analyze propagation through probabilistic methods (epidemiology, network theory, game theory, automata)
a while ago, i wrote some papers on computational semiotics that are at peripherally relevant. The ``Get Stuck'' Theorems show (1) that no matter what finite representational mechanism you use, if you are trying to represent more and more complex phenomena, you will get stuck (the size of the description exceeds your computational capacity to compute with it), and second, that even if humans are adding to a base of knowledge, eventually the knowledge will become too cumbersome to change, mainly because there will be too many interconnections
reference:
Cognitive Technology: Instruments of Mind: 4th International Conference, CT ...
edited by Meurig Beynon, Chrystopher L. Nehaniv, Kerstin Dautenhahn, Springer LNAI 2117 (2001)
the relevance is that a faster increase in knowledge can lead to getting stuck sooner, so it isn't always the most desirable behavior
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