  In the last decade it became apparent that a large number of the most
interesting structures and phenomena of the world can be described by networks:
separable elements, with connections (or interactions) between certain pairs of
them.
  These huge networks pose exciting challenges for the mathematician. Graph
Theory (the mathematical theory of networks) faces novel, unconventional
problems: these very large networks (like the Internet) are never completely
known, in most cases they are not even well defined. Data about them can be
collected only by indirect means like random local sampling.
  Dense networks (in which a node is adjacent to a positive percent of others
nodes) and sparse networks (in which a node has a bounded number of neighbors)
show very different behavior. From a practical point of view, sparse networks
are more important, but at present we have more complete theoretical results
for dense networks. The paper surveys relations with probability, algebra,
extrema graph theory, and analysis.
