REAL
Keystone sector methodology applied to Portugal
could say that the owner and the renter of a house are a dyad as the doctor and their
patients are. Considering these definitions, we established as unity of observation the
individual/entities from whom we have got information through the survey, about their
ties with the other actors/entities presented in the list.
Data can be represented in a graph format, because relational ties have a
direction (arc, defined on the basis of who gives and who receives) and we can design
directed graphs or digraphs, where the entities will be the nodes and the relations will
be the arcs. Formally Robinson and Foulds (1980) define a digraph as:
A digraph is a finite, non-empty set N, whose elements ni= jn1, n2, ..., ng^ are
called nodes, together with a set A = ja12, a13,...a1g,... ag-1, ag∕ of ordered pairs of aj,
called arcs, where ni and nj are distinct members of N.
Nevertheless it is not convenient to represent in a digraph form when the
number N is too large, which is the case.
Adjacency is the expression when we mean two actors are directly related, tied
or connected with one another and formally we could assert that:
“Given actors ni and n in a set of N actors; and A= aij arcs denoting the
existence of relations from actors i to agents j; actors i and j are adjacent if there exist
either of the two arcs aj or aji. Given the digraph D = (NA), its adjacency matrix A(D)
is defined by A(D) = aj, where aij=1 if either aj or aji exists, and aij=0 if otherwise”
(Kilkenny & Nalbart, 2000:9).
In a first step, we studied the density of the entire surveyed network. This
measure compares the existing relationships to all possible relations, which in this case,
will be 6806 (83x82) since N=83. If the complete graph is the one where each actor has
a relationship with all the others, the density will be 100%. In general, the proportion of
the existing numbers of non-reflexive arcs in its possible maximum measures the
density of a digraph. In our case, for each relation R an adjacency matrix (AR) 83 x 83
was constructed with entries aRij = 1 if the ith actor has a relation R tie with the jth actor
and if not, aRij = 0. (Also, aRii = 0).
But actors may be direct or indirectly related through a third element of the
network. To explain this difference in relationships among actors we use the path as a
sequence of arcs from one node to another, which means that in a direct relation there is
only a one-step arc between the nodes and in an indirect relation we can take multi-step
paths into account. This is the way to consider each actor in a network in a richer form
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