My request: I need advice on what to learn in order to solve the following problem.
My problem: I have a network, made up of multiple levels of nodes connected with weighted links. The network is somewhat similar to a hierarchy in that there are fewer nodes in upper levels and more nodes in lower levels. However, it is dissimilar to a hierarchy in that influence and forces of change can flow in it not only from top down, but also from bottom up. This type of network is sometimes called a holarchy. The network changes continuously as a result of interactions with its environment as well as interactions within itself. Changes in the network involve emergence of new nodes and links, as well as modification of weights of links. I receive snapshot images of the network. I want to (1) characterize the change in the network; and (2) find relationships between network change and network configuration.
In the more complicated part of the problem, I have an additional constraint: the network is characterized not only by its links, but also by the location of its nodes.
My problem is abstract.
Where I am: My research so far has led me to complex systems, systems theory, chaos, dissipative structures, holarchy theory and especially its application in electricity grid stability modelling. I am familiar with spatial analysis and somewhat familiar with graph theory and network flow theory. I build Agent-Based Models.
I appreciate any advice that brings me closer to the domains or people that work on the type of problem described above. Also, please feel free to add or correct tags.