9.3 represents the relationship between

9.3 represents the relationship between

General representation of the relationship:

• All relationships are listed;
• To use a {T, F} mapping

Representation of special relationship

• 0-1 matrix (zero-one matrix) is represented;
• There is represented by a directed graph (directed graph)

It shows the relationship with the adjacency matrix

He said 0-1 matrix M _R is the adjacency matrix R, defined as follows:

1. 0-1 by the observation matrix, it is easy to find the following properties:

• Has a reflexive (reflexive) 0-1 matrix main diagonal are all "1"
  
• Have the non-reflexive (irreflexive) 0-1 main diagonal matrix are all "0"
  
• 0-1 principal diagonal matrix has any of symmetry (Symmetric) and symmetrical about the main diagonal elements are equal
  
• 0-1 have any major diagonal matrix inversion symmetry (. Associative), the element on the main diagonal symmetry can not be both "1"
  

1. Definition of two adjoining matrices join a boolean OR operation on these two matrices (boolean 'or')
2. Definition of two adjoining matrices meet a Boolean AND operation of these two matrices (boolean 'and')

Express complex relationships with the 0-1 matrix:

Order M _S◦R = [T _{ij of} ], M _{R & lt} = [R & lt _{ij of} ], M _S = [S _{ij of} ]
the M _S◦R = M _{R & lt} ⊙ M _S
wherein, ⊙ represents two Boolean matrix multiplication (boolean product)

例：

\[ M_R = \left[\begin{matrix} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 0 & 0 \end{matrix} \right] \]
\[ and \quad M_S = \left[\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 1 \end{matrix} \right] \]

The M _S◦R for each t _ij by the M _{R & lt} i-th row and M _S for Boolean j-th column multiplication, the adjacency matrix is obtained S◦R:
\ [S◦R of M_ {} = \ left [ \ begin {matrix} 0 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \ end {matrix} \ right] \]

Boolean matrix multiplication calculator

Chart shows the relationship with

understanding:

• Vertex (vertex)
• 边(arc or edge)
• Digraph (directed graph or digraph)

Example: a relation expressed there using the FIG:

1. And the out-degree of

• A vertex number as a starting point of an arrow: the degree of a vertex
  
• The degree of a vertex: the vertex number of the end point of the arrow a
  

1. Restriction
   If R is defined in the relation of A and B is a subset of A, the limit R (the restriction of R to B) of B is:

   R ∩ (B × B)

2. FIG special properties

• FIG reflexive: Each node has a loopback
  
• Figure has anti-reflexive: no link from point
  
• Figure reflexive: All arrows are bi-directional
  

• FIG reflexive: No double arrow
  

• Special attention: ① not only not anti-symmetric asymmetric map; ② no neither reflexive nor anti-reflexive Fig...

1. Some equivalence relation:

There is a relation R, and its adjacency matrix M _R , △ is provided an equivalence relation, i.e. M _△ is the identity matrix

①. R自反 <= => △ ⊆ R <= => all 1's on its main diagonal
②. R反自反 <= => △ ∩ R = ∅ <= => all 0's on its main diagonal
③. R对称反对称非对称显然不赘述
④. R传递 <= => M_R=[m_ij]具有这个性质:如果m_ij = 1，并且m_jk = 1，那么m_ik = 1.
④. R传递 ==> R² ⊆ R, because if a and c are connected by a path of length 2 in R, then they must be connected by a path of length 1.

1. 误区:

The answer is NO!