Degree of nodal connectivity (to other nodes) is a measure of complexity. Connection is reference (not necessarily “reference” in a semantic sense but at the very least in some coordinate or identity reference to other nodes) and at a global systems level, all reference is systemic self-reference. Complex systems of self-reference (i.e. economies, social systems) generally and autonomously “select for” nodes which have a higher degree or weight value. A secondary degree (beyond that of the number of other nodes any one node connects to) and weight value is that of the aggregated value of the degrees of the nodes connected to any specific node. There is no storage or record in such a system of degrees and weight values; these are just stored in and as the system itself.
The questions of homeostasis and system autopoeisis (i.e. self-generation, self-maintenance) arise at this point: what mechanisms of self-regulation exist to restrain runaway (i.e. cancer-like) growth in any specific self-referential, self-gravitating system ? Economic and information technology or communications systems themselves appear to be hell-bent on endless growth and internal complexity on an asymptotic curve tending towards an aspirational singularity of some sort. It may be that the internal, structural complexity and degree-value burden on any specific node may eventually reach peak saturation and that this is an implicit constraint on system growth. Rising preponderance towards anxiety-based disorders may indicate ways in which individual human beings in many cultures are already reaching peak complexity saturation in regards to psychological balance and well-being as a response to (also) being embodied nodes in such a vast system of complex self-reference.
The solution to any notional peak nodal complexity is undoubtedly that of systemic reorganisation and reconfiguration at a connectivity-rules, degrees/weight-values or systems-axiomatic level. There is always a way to logically extend a system and there are as a matter of probability also useful and constructive, creative or innovative ways to reorganise this rolling disaster of human disorganisation within which we are all embedded as participants. Identifying uself axioms and systems-primitives seems to me to be of critical importance as a starting point for this venture.