Reference #: 00546

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**Invention Description:

The subject invention is a method for the reduction of large network connection matrices to far less numbers of variables, thus constituting an invention of new "entropy matrices for the network".

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**Potential Applications:

The use of such intellectual property or technology is for the classification and tracking of the behavior of complex systems over time to identify failures, attacks, major structural changes in the topology, and other variance within Internet Networks.

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**Advantages and Benefits:

Reduction of large networks to a few representative parameters, which makes it possible to reduce their mathematical complexity, distills this vast array of values to a representative summary set of "network metrics" that can effectively track the systems.

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**Background:

By *network*, one means a set of points, called nodes, which are numbered sequentially by integers (1, 2,…N). The network itself is then defined by a non-negative number or "connection" between nodes i and j as C_{ij}. The example of airline networks, with airports as the nodes numbered 1,2,…N, can be chosen where the number of flights per month between cities or the number of passengers transported between the two cities per month are designated as the weights C_{ij}, defining the network. For large networks, it is a problem of extraordinary mathematical complexity to (a) compare two networks to see if they are the same (or "close"), (b) classify a network by its topological structure, or (c) follow a rapidly changing network to see if it has highly usual behavior or is behaving "normally" (such as Internet traffic). The number of nodes of a network of one million points is the square of that number, or 1 trillion values. If these values are changing every second (as in the internet), it is of the greatest importance to be able to distill this vast array of values to a representative summary set of "network metrics". The problem is similar to the reduction of the 10^{24} positions and velocities of the molecules in a gas, down to a few variables such as pressure, temperature, internal energy, entropy, etc., such as one can accomplish using the sciences of thermodynamics and statistical mechanics.