Networks/Theory III

Only a fast and global transformation towards decarbonization and sustainability can keep the Earth in a civilization-friendly state. Cities play an important role in this transformation: they are responsible for a dis-proportionally large part of greenhouse gas emissions, and simultaneously are one of the main drivers of sustainable policy innovation and adoption. Learning from each other to reduce, prepare for and react to the coming environmental changes, they can be conceptualized as nodes in a globe-spanning network.

Patterns are macroscopic structures which are derived from the self-organization of a system consisting of macroscopic interacting entities. The formation of spatial patterns was originally based on the competition between fast diffusing chemicals, the inhibitors, and the slow diffusing activators. This theory originally assumed a continuous space, but we now know that if one looks closely, many systems are discrete, and can be abstracted as a network. One such system is the brain, which can be described as a network of connected neurons.

In complex networks, the degree distribution of the nodesis known to be non-homogeneous with a heavy tail. Consequently, a small set of nodes (called hubs) are highly connected while the vast majority share few connections with their neighbors. The community structure is another main topological feature of many real-world networks. In these networks, the nodes shared by more than one community are called overlapping nodes. They play an important role in the network dynamics due to their ability to reach multiple communities [1].

Interactions between elements, which are usually represented by networks, have to delineate potentially unequal relationships in terms of their relative importance or direction. The intrinsic unequal relationships of such kind, however, are opaque or hidden in numerous real systems. For instance, when a node in a network with limited interaction capacity spends its capacity to its neighboring nodes, the allocation of the total amount of interactions to them can be vastly diverse.