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From Apache Wiki <wikidi...@apache.org>
Subject [Hama Wiki] Update of "GraphAndMatrices" by udanax
Date Thu, 06 Nov 2008 13:42:44 GMT
Dear Wiki user,

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The following page has been changed by udanax:
http://wiki.apache.org/hama/GraphAndMatrices

------------------------------------------------------------------------------
- Describe GraphAndMatrices here.
+ == Matrices ==
+ We can record who is connected to whom on a given social relation via an adjacency matrix.
The adjacency matrix is a square, 1-mode matrix like this:
  
+ ||   || A || B || C || D || E || F || G ||
+ || A ||   || 1 || 0 || 1 || 0 || 0 || 1 ||
+ || B || 1 ||   || 1 || 0 || 1 || 0 || 0 ||  
+ || C || 1 || 1 ||   || 1 || 1 || 0 || 0 ||
+ || D || 1 || 1 || 1 ||   || 0 || 0 || 0 ||
+ || E || 0 || 0 || 0 || 1 ||   || 1 || 0 ||
+ || F || 0 || 0 || 0 || 0 || 1 ||   || 0 ||
+ || G || 1 || 1 || 0 || 0 || 0 || 0 ||   ||
+ 
+ [http://wiki.apache.org/hama-data/attachments/BigTableForGmail/attachments/graph.jpg]
+ 
+ If the matrix as a whole is called X, then the contents of any given cell are denoted x,,ij,,.
For example, in the matrix above, x,,ij,, = 1, because A likes B. Note that this matrix is
not quite symmetric (x,,ij,, not always equal to x,,ji,,).
+ 
+ Anything we can represent as a graph, we can also represent as a matrix. For example, if
it is a valued graph, then the matrix contains the values instead of 0s and 1s.
+ 
+ By convention, we normally record the data so that the row person "does it to" the column
person. For example, if the relation is "gives advice to", then x,,ij,, = 1 means that person
i gives advice to person j, rather than the other way around. However, if the data not entered
that way and we wish it to be so, we can simply transpose the matrix. The transpose of a matrix
X is denoted X'. The transpose simply interchanges the rows with the columns.
+ 

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