My mother always said that nothing with a "too" in front of it is good. That is certainly true about connectivity, too little and too much can be equally detrimental. High levels of connectivity can facilitate the fast recovery of a system after a disruption, but at the same time some disruptions spread faster in highly connected or closely coupled systems.
Connectivity refers to the nature and strength of interactions between various components/parts of the system. Closely coupled systems are interdependent and highly connected vs loosely coupled or decoupled systems that have little or no interdependence.
In organisations, close coupling or high levels of connectivity is often seen as desirable as it contributes to the effective flow of information across organisational boundaries. Higher levels of interdependence may also lead to better relationships and morale, facilitate learning and reduce unnecessary duplication. In general, a highly connected organisation is able to respond to a disruption quickly and effectively, however this fast response may not always be positive. For example, in tightly coupled systems with high levels of interdependence, the failure of one node could lead to rapid failure in others. We often see this in workplace accidents where one failure seems to trigger a domino effect that quickly leads to a catastrophic event. That same network that allows for the easy flow of useful information to facilitate agility can also facilitate the flow of negative sentiment and rumours, spreading discontent or disruptive untruths quickly and effectively across the system.
Loosely coupled or decoupled systems have fewer tight links between parts and therefore are able to absorb failures or unplanned behavior without as much destabilisation. It's easy to see how in some contexts limited connectivity or loose coupling can be of benefit to a system as it provides a barrier to the domino like spread of disturbances e.g. forest fires or infectious diseases. However, being too loosely coupled has disadvantages too - most often expressed in complaints about "silo mentalities". In short, in loosely coupled systems information flow is often inhibited; personal relationships are non-existent or few and far between and unnecessary duplication abounds. In some organisations it leads to completely divergent sub-cultures and unhealthy internal competition.
A key consideration therefore becomes what the optimal level of connectivity or coupling is for your particular system. Methodologies like Social Network Analysis might provide some insight into the current state of connectedness in the system, although complex adaptive systems change the moment they are looked at or analysed, so I'm not always convinced that these kinds of diagnostics add real value (I've used SNA myself in the past with varying degrees of success). I doubt that diagnosis is as important as intervention in many large corporates, as my experience is that most have become too loosely coupled and silod as they have grown in size and complexity. Here the key thing is not mapping existing networks, but increasing overall levels of connectivity to facilitate a more effective flow of information and greater agility, without over connecting the system. One of the best techniques I've seen for this is Social Network Stimulation, developed by Prof Dave Snowden (read more about it here).
Whenever we intervene in organisations to increase or decrease connectivity we need to be very intentional and really think about what we are doing as these kinds of interventions often have unintended consequences. Whenever I hear people talk about "breaking down silos" I cringe, because those silos are often well functioning business units or teams that have simply become too closely connected internally and too loosely connected externally. Do you really want to break your finance division? You need specialised units (or silos) for your organisation to be effective, we simply need the boundaries between these silos to be permeable and foster greater external connectivity to other areas.
So, as stated in the title when it comes to connectivity there is not one right answer to the question how much is enough. We need to keep in mind the Goldilocks principle, the porridge must be not too hot, not too cold, but just right ... for your particular context.