  There is an abundance of literature on complex networks describing a variety
of relationships among units in social, biological, and technological systems.
Such networks, consisting of interconnected nodes, are often self-organized,
naturally emerging without any overarching designs on topological structure yet
enabling efficient interactions among nodes. Here we show that the number of
nodes and the density of connections in such self-organized networks exhibit a
power law relationship. We examined the size and connection density of 47
self-organizing networks of various biological, social, and technological
origins, and found that the size-density relationship follows a fractal
relationship spanning over 6 orders of magnitude. This finding indicates that
there is an optimal connection density in self-organized networks following
fractal scaling regardless of their sizes.

Adaptation and Self-Organizing Systems