2.1 Cyberspace representation

### 2.1.2 Spatial representation

The dissimilarity between two resources can be defined by the length of the shortest edge-sequence (path) between them:

with
,
,
,

and
.

This is in fact the geodesic distance and it can be calculated by building a power matrix, starting with . When , the power matrix is the adjacency matrix, so that if , the resources are adjacent, and the distance between them equals . If and , then the shortest path is of length 2 and so forth. Consequently, the first power for which the is non-zero gives the length of the edge-sequence and is equal to . Mathematically,
.

Note that is the number of paths between the resources and .

With such a metric defined, it is possible to construct a distance (dissimilarity) matrix of the graph , composed of vectors of dimensions. Therefore, each vector gives an unique representation of each resource as a point in an -dimensional space.

Cyberspace geography visualization - 15 October 1995

Luc Girardin, The Graduate Institute of International Studies