# Measuring Network Complexity

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## Organized Complexity

Three different measures of network complexity have been examined at this point: NCI, modeling design complexity, and NetComplex. Each of these attempts to measure, in some way, at least some component of the four realms of network complexity—state, speed, surface, and optimization. None of them, however, measure everything in any one of these three domains, and none of them even come close to measuring overall network complexity. Why? The problem isn’t just the ability to measure and process all the information needed to produce a single complexity number, it’s embedded in the problem of network complexity itself.

Imagine, for a moment, a pool table with a set of balls on it. These specific balls are (at least nearly) perfect in their resilience, so they lose only infinitely small amounts of energy when they strike another object, and the bumpers on the sides of the table are designed in much the same way. There are no pockets in this table, either, so there is no place for the balls to leave the table. Now, place the balls on the table in some random distribution, and then strike one so it starts a chain reaction. The result will be a statistically random set of movements, each ball moving about the table, striking another ball or a bumper, retaining most of its energy, and then moving in a straight line in some other direction.

This particular problem is ripe for statistical regression analysis, or any other form of analysis data science can provide. The data scientist can tell you, based on a set of derived formulas, how often one ball will strike another, how long the system will take to run out of energy, what patterns will form in the randomly moving balls at what time—and many other things. Data science excels at finding patterns in seemingly random bits of data. In fact, it is often found that the data set must be larger to make an accurate prediction; the larger the data set, the more accurate characterization of it can be made, and the more accurate the predictions about the state of that data at some specific point in the future will be.

But let’s change the situation somewhat. Let’s take the same pool table, the same balls—all the same physical conditions. Only this time, someone has preplanned the position and movement of every ball such that no two balls strike one another, even though they are all in motion. In fact, the movement of every ball is identical throughout the entire time the balls are in motion.

Simple observation can tell us which ball will be where at any point in time. Simple observation might even be able to provide a formula telling us where there will be clumps of balls on the table, or near misses. But statistical analysis cannot go much beyond a few simple facts here. What’s more interesting is that statistical analysis cannot tell us what the point is in having these balls arranged just this way.

• This is the problem of organized complexity.
• As Warren Weaver noted in 1948:
• This new method of dealing with disorganized complexity, so powerful an advance over the earlier two-variable methods, leaves a great field untouched. One is tempted to oversimplify, and say that scientific methodology went from one extreme to the other—from two variables to an astronomical number—and left untouched a great middle region. The importance of this middle region, moreover, does not depend primarily on the fact that the number of variables involved is moderate—large compared to two, but small compared to the number of atoms in a pinch of salt. The problems in this middle region, in fact, will often involve a considerable number of variables. The really important characteristic of the problems of this middle region, which science has as yet little explored or conquered, lies in the fact that these problems, as contrasted with the disorganized situations with which statistics can cope, show the essential feature of organization. In fact, one can refer to this group of problems as those of organized complexity.6

This field of organized complexity exactly describes the situation engineers face in looking at computer networks. No matter what angle a computer network is approached from, the problem is both complex and organized.

• Protocols are designed with a specific set of goals in mind, a specific mindset about how the problems approached should be solved, and a set of tradeoffs between current optimal use, future flexibility, supportability, and ease of implementation.
• Applications that run on top of a network are designed with a specific set of goals in mind.
• Control planes that provide the metadata that make a computer network work are designed with a specific set of goals in mind.
• Protocols that carry information through the network, at every level, are designed with a specific set of goals in mind.

No matter which system within computer network is considered—from protocols to design to applications to metadata—each one was designed with a specific set of goals, a specific mindset about how to solve the problems at hand, and a specific set of tradeoffs. Some of these might be implicit, rather than explicit, but they are, nonetheless, intentional goals or targets.

A network is not just a single system that exhibits organized complexity, but a lot of different interlocking systems, each of which exhibits organized complexity, and all of which combined exhibit a set of goals as well (perhaps a more ephemeral set of goals, such as “making the business grow,” but a set of goals nonetheless).

Network complexity, then, cannot simply be measured, computed, and “solved,” in the traditional sense. Even everything could be measured in a single network, and even if all the information gathered through such measurement could be processed in a way that made some sense, it would still not be possible to fully express the complexity of a computer network in all its myriad parts—in essence because there is no way to measure or express intent.

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