edu.uci.ics.jung.algorithms.metrics.StructuralHoles<V,E>
|
||||||||||
| PREV CLASS NEXT CLASS | FRAMES NO FRAMES | |||||||||
| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD | |||||||||
java.lang.Object
public class StructuralHoles<V,E>
Calculates some of the measures from Burt's text "Structural Holes: The Social Structure of Competition".
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.
| Field Summary | |
|---|---|
protected org.apache.commons.collections15.Transformer<E,? extends Number> |
edge_weight
|
protected Graph<V,E> |
g
|
| Constructor Summary | |
|---|---|
StructuralHoles(Graph<V,E> graph,
org.apache.commons.collections15.Transformer<E,? extends Number> nev)
Creates a StructuralHoles instance based on the
edge weights specified by nev. |
|
| Method Summary | |
|---|---|
double |
aggregateConstraint(V v)
The aggregate constraint on v. |
double |
constraint(V v)
Burt's constraint measure (equation 2.4, page 55 of Burt, 1992). |
double |
effectiveSize(V v)
Burt's measure of the effective size of a vertex's network. |
double |
efficiency(V v)
Returns the effective size of v divided by the number of
alters in v's network. |
double |
hierarchy(V v)
Calculates the hierarchy value for a given vertex. |
double |
localConstraint(V v1,
V v2)
Returns the local constraint on v from a lack of primary holes
around its neighbor v2. |
protected double |
maxScaledMutualEdgeWeight(V v1,
V v2)
The marginal strength of v1's relation with contact vertex2. |
protected double |
mutualWeight(V v1,
V v2)
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. |
protected double |
normalizedMutualEdgeWeight(V v1,
V v2)
Returns the proportion of v1's network time and energy invested
in the relationship with v2. |
protected double |
organizationalMeasure(Graph<V,E> g,
V v)
A measure of the organization of individuals within the subgraph centered on v. |
| Methods inherited from class java.lang.Object |
|---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| Field Detail |
|---|
protected org.apache.commons.collections15.Transformer<E,? extends Number> edge_weight
protected Graph<V,E> g
| Constructor Detail |
|---|
public StructuralHoles(Graph<V,E> graph,
org.apache.commons.collections15.Transformer<E,? extends Number> nev)
StructuralHoles instance based on the
edge weights specified by nev.
| Method Detail |
|---|
public double effectiveSize(V v)
v'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
normalizedMutualEdgeWeight(Object, Object),
maxScaledMutualEdgeWeight(Object, Object)public double efficiency(V v)
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 constraint(V v)
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.
localConstraint(Object, Object)public double hierarchy(V v)
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())
localConstraint(Object, Object),
aggregateConstraint(Object)
public double localConstraint(V v1,
V v2)
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
normalizedMutualEdgeWeight(Object, Object)public double aggregateConstraint(V v)
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)
protected double organizationalMeasure(Graph<V,E> g,
V v)
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 normalizedMutualEdgeWeight(V v1,
V v2)
v1'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.
mutualWeight(Object, Object)
protected double mutualWeight(V v1,
V v2)
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 maxScaledMutualEdgeWeight(V v1,
V v2)
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.
mutualWeight(Object, Object)
|
||||||||||
| PREV CLASS NEXT CLASS | FRAMES NO FRAMES | |||||||||
| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD | |||||||||