public class StructuralHoles<V,E> extends Object
Notes:
Transformer
instance.
Based on code donated by Jasper Voskuilen and Diederik van Liere of the Department of Information and Decision Sciences at Erasmus University.
Modifier and Type | Field and Description |
---|---|
protected com.google.common.base.Function<E,? extends Number> |
edge_weight |
protected Graph<V,E> |
g |
Constructor and Description |
---|
StructuralHoles(Graph<V,E> graph,
com.google.common.base.Function<E,? extends Number> nev) |
Modifier and Type | Method and Description |
---|---|
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
v1 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 v2.
|
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 . |
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
v
- the vertex whose properties are being measurednormalizedMutualEdgeWeight(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.v
- the vertex whose properties are being measuredpublic 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.
v
- the vertex whose properties are being measuredlocalConstraint(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())
v
- the vertex whose properties are being measuredlocalConstraint(Object, Object)
,
aggregateConstraint(Object)
public double localConstraint(V v1, V v2)
v1
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) ) )^2where
N(v) = v.getNeighbors()
p(v,w) =
normalized mutual edge weight of v and w
v1
- the first vertex whose local constraint is desiredv2
- the second vertex whose local constraint is desirednormalizedMutualEdgeWeight(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)
v
- the vertex whose properties are being measuredprotected 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.
g
- the subgraph centered on vv
- the vertex whose properties are being measuredprotected 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
.v1
- the first vertex of the pair whose property is being measuredv2
- the second vertex of the pair whose property is being measuredmutualWeight(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
.v1
- the first vertex of the pair whose property is being measuredv2
- the second vertex of the pair whose property is being measured<v2, v1>
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
.v1
- the first vertex of the pair whose property is being measuredv2
- the second vertex of the pair whose property is being measuredmutualWeight(Object, Object)
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