Feedback between node and network dynamics can produce real-world network properties

Real-world networks are characterized by common features, including among others a scale-free degree distribution, a high clustering coefficient and a short typical distance between nodes. These properties are usually explained by the dynamics of edge and node addition and deletion. In a different context, the dynamics of node content within a network has been often explained via the interaction between nodes in static networks, ignoring the dynamic aspect of edge addition and deletion. We here propose to combine the dynamics of the node content and of edge addition and deletion, using a threshold automata framework. Within this framework, we show that the typical properties of real-world networks can be reproduced with a Hebbian approach, in which nodes with similar internal dynamics have a high probability of being connected. The proper network properties emerge only if an imbalance exists between excitatory and inhibitory connections, as is indeed observed in real networks. We further check the plausibility of the suggested mechanism by observing an evolving social network and measuring the probability of edge addition as a function of the similarity between the contents of the corresponding nodes. We indeed find that similarity between nodes increases the emergence probability of a new link between them. The current work bridges between multiple important domains in network analysis, including network formation processes, Kaufmann Boolean networks and Hebbian learning. It suggests that the properties of nodes and the network convolve and can be seen as complementary parts of the same process.