theory of network

[AntonioLao]

The theory of network by itself is a branch of topology. This theory is sometimes found under the general heading of graph theory. The word ‘network’ connotes its meaning with electrical networks. However, a good representative of a topological network is still the map designed to show the London Underground. It is topological simply because its design uses rubber-sheet geometry. It is not drawn to any scale or proportion, the distances between train stations are wrong, east-west lines could actually indicates north-south lines, vice versa; but what is correct are the relative position between landmarks and stations and the connections among these stations. Using similar terminologies from electrical circuits, the connections between stations are called edges or branches. The stations are called vertices or nodes. Consequently, each edge can only connect two vertices. Although the curving wiggly shape and length of each connection is not important, the associated functional numeric or signed notation is, such that each edge is assigned a function number or sign (plus or minus). This could mean time duration or capacity for processing data flow or action or positive or negative attitude of any behavioral connection.


An example is now given for modeling the network between five urbanized cities by the vertex set: {v1, v2, v3, v4, v5} and the edge set: {v1v2, v1v3, v1v4, v1v5, v2v3, v2v4, v2v5, v3v4, v3v5, v4v5} with the following arbitrary function set of distances between them: {(v1v2, 23), (v1v3, 5), (v1v4, 10), (v1v5, 70), (v2v3, 44), (v2v4, 15), (v2v5, 31), (v3v4, 9), (v3v5, 60), (v4v5, 25)}. The function set indicates that the distance between city 1 and city 2 is 23, between city 1 and city 3 is 5, so on and so forth. However, these can also be represented by a 5 by 5 matrix. The row and column indexes are denoted by the 5 vertices and the distances are the elements of this matrix. Since the distance for each city between itself is zero, the trace of the matrix is zero, indicated by the sum of the elements along the main diagonal. These demonstrate the mathematical fact that every topology can be represented by matrices of different orders or dimensions. But for a quantum theory of the spacetime continuum, the vertices are given either by an H-plus or an H-minus, which can span the totality of the spacetime continuum as the most complex network of physical reality.

[mkirkpatrick]

Very interesting idea here Antonio,and using railways to express it is novel,I worked for the railway in the UK for a number of years in the swinging sixties and am familiar with the network idea.


regards michael.

[AntonioLao]

I copied the idea from Keith Devlin who wrote a book about the Millennium Prizes of solving the ten unsolved problems of mathematics and science. The purpose of this thread to show the relation between network and topology which are described by matrices. I'm using Hadamard matrices to describe the network of the spacetime continuum.

[mkirkpatrick]

I copied the idea from Keith Devlin who wrote a book about the Millennium Prizes of solving the ten unsolved problems of mathematics and science.

There is only one puzzle we must solve and that is DCF.

regards michael.

[AntonioLao]

Then the other ten must be related to DCF, it was once said that all roads lead to Rome. This is during the peak of the Roman Empire.

[mkirkpatrick]

Then the other ten must be related to DCF, it was once said that all roads lead to Rome. This is during the peak of the Roman Empire.

That is long gone now,maybe in the near future all roads will lead to DCF.


regards michael.

[AntonioLao]

If it is a technological success then all roads of progress come out of DCF.

[mkirkpatrick]

If it is a technological success then all roads of progress come out of DCF.

The world needs to focus on DCF for its use will bring salvation to mankind and hope for the third world.


regards michael.

[AntonioLao]

Since the global network is connected by the internet, understanding the topology of the internet is crucial for solving the problems of the world.

[mkirkpatrick]

Since the global network is connected by the internet, understanding the topology of the internet is crucial for solving the problems of the world.

We are all interconnected with each other as well.we need to somehow work together,maybe the internet can help in this?

regards michael.