Notes: - *
Transformer instance.
- * Nonexistent edges are treated as edges with weight 0 for purposes
- * of edge weight calculations.
- * Based on code donated by Jasper Voskuilen and - * Diederik van Liere of the Department of Information and Decision Sciences - * at Erasmus University.
- * - * @author Joshua O'Madadhain - * @author Jasper Voskuilen - * @see "Ronald Burt, Structural Holes: The Social Structure of Competition" - * @author Tom Nelson - converted to jung2 - */ -public class StructuralHolesStructuralHoles instance based on the
- * edge weights specified by nev.
- */
- public StructuralHoles(Graphv's neighbor set,
- * not counting ties to v. Formally:
- *
- * effectiveSize(v) = v.degree() - (sum_{u in N(v)} sum_{w in N(u), w !=u,v} p(v,w)*m(u,w))
- *
- * where
- * N(a) = a.getNeighbors()
- * p(v,w) = normalized mutual edge weight of v and w
- * m(u,w) = maximum-scaled mutual edge weight of u and w
- * v divided by the number of
- * alters in v's network. (In other words,
- * effectiveSize(v) / v.degree().)
- * If v.degree() == 0, returns 0.
- */
- public double efficiency(V v) {
- double degree = g.degree(v);
-
- if (degree == 0)
- return 0;
- else
- return effectiveSize(v) / degree;
- }
-
- /**
- * Burt's constraint measure (equation 2.4, page 55 of Burt, 1992). Essentially a
- * measure of the extent to which v is invested in people who are invested in
- * other of v's alters (neighbors). The "constraint" is characterized
- * by a lack of primary holes around each neighbor. Formally:
- *
- * constraint(v) = sum_{w in MP(v), w != v} localConstraint(v,w)
- *
- * where MP(v) is the subset of v's neighbors that are both predecessors and successors of v.
- * @see #localConstraint(Object, Object)
- */
- public double constraint(V v) {
- double result = 0;
- for(V w : g.getSuccessors(v)) {
-
- if (v != w && g.isPredecessor(v,w))
- {
- result += localConstraint(v, w);
- }
- }
-
- return result;
- }
-
-
- /**
- * Calculates the hierarchy value for a given vertex. Returns NaN when
- * v's degree is 0, and 1 when v's degree is 1.
- * Formally:
- *
- * hierarchy(v) = (sum_{v in N(v), w != v} s(v,w) * log(s(v,w))}) / (v.degree() * Math.log(v.degree())
- *
- * where
- * N(v) = v.getNeighbors()
- * s(v,w) = localConstraint(v,w) / (aggregateConstraint(v) / v.degree())
- * v from a lack of primary holes
- * around its neighbor v2.
- * Based on Burt's equation 2.4. Formally:
- *
- * localConstraint(v1, v2) = ( p(v1,v2) + ( sum_{w in N(v)} p(v1,w) * p(w, v2) ) )^2
- *
- * where
- * N(v) = v.getNeighbors()
- * p(v,w) = normalized mutual edge weight of v and w
- * v. Based on Burt's equation 2.7.
- * Formally:
- *
- * aggregateConstraint(v) = sum_{w in N(v)} localConstraint(v,w) * O(w)
- *
- * where
- * N(v) = v.getNeighbors()
- * O(w) = organizationalMeasure(w)
- * v. Burt's text suggests that this is
- * in some sense a measure of how "replaceable" v is by
- * some other element of this subgraph. Should be a number in the
- * closed interval [0,1].
- *
- * This implementation returns 1. Users may wish to override this - * method in order to define their own behavior.
- */ - protected double organizationalMeasure(Graphv1's network time and energy invested
- * in the relationship with v2. Formally:
- * - * normalizedMutualEdgeWeight(a,b) = mutual_weight(a,b) / (sum_c mutual_weight(a,c)) - *- * Returns 0 if either numerator or denominator = 0, or if
v1 == v2.
- * @see #mutualWeight(Object, Object)
- */
- protected double normalizedMutualEdgeWeight(V v1, V v2)
- {
- if (v1 == v2)
- return 0;
-
- double numerator = mutualWeight(v1, v2);
-
- if (numerator == 0)
- return 0;
-
- double denominator = 0;
- for (V v : g.getNeighbors(v1)) {
- denominator += mutualWeight(v1, v);
- }
- if (denominator == 0)
- return 0;
-
- return numerator / denominator;
- }
-
- /**
- * Returns the weight of the edge from v1 to v2
- * plus the weight of the edge from v2 to v1;
- * if either edge does not exist, it is treated as an edge with weight 0.
- * Undirected edges are treated as two antiparallel directed edges (that
- * is, if there is one undirected edge with weight w connecting
- * v1 to v2, the value returned is 2w).
- * Ignores parallel edges; if there are any such, one is chosen at random.
- * Throws NullPointerException if either edge is
- * present but not assigned a weight by the constructor-specified
- * NumberEdgeValue.
- */
- protected double mutualWeight(V v1, V v2)
- {
- E e12 = g.findEdge(v1,v2);
- E e21 = g.findEdge(v2,v1);
- double w12 = (e12 != null ? edge_weight.transform(e12).doubleValue() : 0);
- double w21 = (e21 != null ? edge_weight.transform(e21).doubleValue() : 0);
-
- return w12 + w21;
- }
-
- /**
- * The marginal strength of v1's relation with contact vertex2.
- * Formally:
- * - * normalized_mutual_weight = mutual_weight(a,b) / (max_c mutual_weight(a,c)) - *- * Returns 0 if either numerator or denominator is 0, or if
v1 == v2.
- * @see #mutualWeight(Object, Object)
- */
- protected double maxScaledMutualEdgeWeight(V v1, V v2)
- {
- if (v1 == v2)
- return 0;
-
- double numerator = mutualWeight(v1, v2);
-
- if (numerator == 0)
- return 0;
-
- double denominator = 0;
- for (V w : g.getNeighbors(v1)) {
-
- if (v2 != w)
- denominator = Math.max(numerator, mutualWeight(v1, w));
- }
-
- if (denominator == 0)
- return 0;
-
- return numerator / denominator;
- }
-}