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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 actor by actor matrix like this:
<ac:structured-macro ac:name="unmigrated-wiki-markup" ac:schema-version="1" ac:macro-id="6cfdfe28-ee95-427c-9a69-408d1c467a3e"><ac:plain-text-body><![CDATA[ |
| A | B | C | D | E | F | G | [http://wiki.apache.org/hama-data/attachments/GraphAndMatrices/attachments/graph.jpg]]]></ac:plain-text-body></ac:structured-macro> |
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 |
|
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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 xij = 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.
Matrix Algebra
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See \[:Architecture: Hama Architecture & Overview\]