Closeability

Introduction
A VIAAC's closeability is a description of its ability to survive without external inputs. In the flow network model, closeability is a measure of the number of inputs and outputs from and to a certain entity or category (such as the ecosystem or outside markets).

A closeable VIAAC is similar to an autarky in that it is able to survive without relying on external inputs/outputs. However, an autarky is a description of both the ability and the state of being closed off from external inputs/outputs, hence "closeability" rather than "closed". Having the ability to operate as a closed community provides disaster protection, but may not provide the same quality of life or performance as an open community. Closeability strikes a balance between the two, as well as providing more detailed qualification than just closed or open.

Definitions
A VIAAC IS:
 * Input closeable if it can survive with no inputs except its own (but with outputs to the outside). This can describe any subtype of closeability, e.g. fully input closeable.
 * Output closeable if it can survive with no outputs except its own (but with inputs from the outside). This can describe any subtype of closeability, e.g. market output closeable.
 * Pseudo-closeable (of degree n) if it can become closeable in n steps (or clock cycles). This can describe any subtype of closeability, e.g. pseudo-market closeable of degree n.
 * Quasi-closeable if it can survive with only inputs or outputs from other VIAACs or non-market economies. A quasi-closeable VIAAC is pseudo-quasi-closeable of degree 0.
 * Semi-closeable if it can survive with only inputs or outputs from other VIAACs. All semi-closeable VIAACs are also quasi-closeable.
 * Fully-closeable if it can survive with no inputs or outputs except its own. All fully-closeable VIAACs are also semi-closeable.

The edge from a VIAAC or VIAAC network to an outside economy (another VIAAC, VIAAC network, market, and so on) is critical. Thus, closeability describes the presence or absence of critical edges. Any flow of resources that contains a critical edge is called a critical path. A critical path in which there is a path from a vertex to itself is a critical cycle.

Which Type a VIAAC Should Target
The type of closeability that should be aimed for depends on the community's current status and environment. One in a harsh, disaster-prone, or otherwise risky environment should be fully closeable. One that has activity with other VIAACs may wish to remain only quasi-closeable. Each VIAAC will have to analyze its individual situation, disaster risk, and the risk of its neighbors to determine which goal will fit the best. It is likely that adjacent VIAACs will have similar closeability goals.

Network Closeability vs. Individual Closeability
Nearby VIAACs, assuming they themselves are stable and connected, provide an additional trophic level whose closeability as a network can be different (usually stricter) than that of the individual communities. This will be affected by logistic conditions, such as which VIAACs in a group are logistically connected. If an individual VIAAC in a network has degree greater than two (it is connected to three or more others), then it may be able to relax its closeability conditions, such that a group of four that is fully closeable on the aggregate may be semi-closeable individually. For further development, a group of 9 VIAACs that form a web or antiweb (each VIAAC is connected to 4 others) can be degree 1 pseudo-closeable; If they form an antihole (each VIAAC is a chord/each VIAAC is connected to 6 others), this can be relaxed to degree 3 pseudo-closeable. This is an oversimplification, as each VIAAC may have different conditions that influence its goal, but it's a starting point to think about the network effects.