Agriculture Reference
In-Depth Information
At all the study sites, participants began by listing categories of concepts needed
to explain the relationships between, on the one hand, agroecosystem problems and
concerns and, on the other, its health and sustainability. A metaphor in the local
language was used to equate categories of related concepts to pots and the thought
process as cooking. Categories, and eventually the concepts themselves, were gen-
erated using declarative statements of the form, “You cannot cook (think about) x
without (including the concept of) y.” Concepts belonging to the same “pot”—those
seen to be related in some ways—were circled if on a chalkboard or put in one pile
if on cards. Relationships between pots were then added to the diagram, followed by
relationships within.
4.2.2 g e o m e t r i C A n A l y s e s
A signed digraph D = ( V , A ) was defined as consisting of a set ( V ) of points ( v 1 , v 2 ,
…, v n ) called vertices and another set ( A ) of dimensions n × n called the adjacency
matrix (Figure 4.1). The adjacency matrix of a digraph D = ( V , A ) consists of ele-
ments a ij , where a ij = 1 if the arc ( v i , v j ) exists and 0 if the arc ( v i , v j ) does not exist,
with i and j = {1, 2, 3, …, n }. The in-degree of a vertex ( v i ) is the sum of the column
( i ) in the adjacency matrix corresponding to that vertex. Conversely, the out-degree
of a vertex ( v i ) is the sum of the row ( i ) in the adjacency matrix corresponding to that
vertex. The sum of the in-degree and the out-degree of a vertex is the total degree
( td ) and is a measure of the cognitive centrality of the vertex (Nozicka et al., 1976).
A vertex with an in-degree of 0 was described as a source, while one with an out-
degree of 0 was described as a sink.
A path was defined as a sequence of distinct vertices ( v 1 , v 2 , …, v t ) connected by
arcs such that for all i = {1, 2, ..., t } there is an arc ( v i , v i +1 ). The sign (or effect) of a
path was the product of the signs of its arcs, and the length of a path was the number
of arcs in it. The impact of a path from vertex v i to another vertex v j was calculated
as the effect of the path multiplied by the sign of vertex v j . The sign of a vertex was
v 1
v 2
v 3
v 4
OD
v 1
0
1
0
1
2
V 1
A
v 2
0
0
1
1
2
v 3
0
0
0
1
1
v 4
0
0
0
0
0
V 2
ID
0
1
1
3
0
-1
0
0
D
Sgn(A)
0
0
1
1
0
0
0
-1
1
0
0
0
V 3
V 4
4
fIGuRe 4.1 Example of a digraph and its adjacency ( A ) and signed adjacency (sgn( A ))
matrices. See CD for color image.
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