edu.uci.ics.jung.algorithms.metrics

Class StructuralHoles<V,E>

java.lang.Object

edu.uci.ics.jung.algorithms.metrics.StructuralHoles<V,E>

public class StructuralHoles<V,E>
extends java.lang.Object

Calculates some of the measures from Burt's text "Structural Holes: The Social Structure of Competition".

Notes:

• Each of these measures assumes that each edge has an associated non-null weight whose value is accessed through the specified 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.

See Also:

"Ronald Burt, Structural Holes: The Social Structure of Competition"

Constructor Summary

Constructors

Constructor and Description
StructuralHoles(Graph<V,E> graph, com.google.common.base.Function<E,? extends java.lang.Number> nev)

Method Summary

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.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

StructuralHoles

public StructuralHoles(Graph<V,E> graph,
                       com.google.common.base.Function<E,? extends java.lang.Number> nev)

Parameters:

graph - the graph for which the metrics are to be calculated

nev - the edge weights

Method Detail

effectiveSize

public double effectiveSize(V v)

Burt's measure of the effective size of a vertex's network. Essentially, the number of neighbors minus the average degree of those in 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

Parameters:

v - the vertex whose properties are being measured

Returns:

the effective size of the vertex's network

See Also:

normalizedMutualEdgeWeight(Object, Object), maxScaledMutualEdgeWeight(Object, Object)

efficiency

public double efficiency(V v)

Returns the effective size of v divided by the number of alters in v's network. (In other words, effectiveSize(v) / v.degree().) If v.degree() == 0, returns 0.

Parameters:

v - the vertex whose properties are being measured

Returns:

the effective size of the vertex divided by its degree

constraint

public double constraint(V v)

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.

Parameters:

v - the vertex whose properties are being measured

Returns:

the constraint of the vertex

See Also:

localConstraint(Object, Object)

hierarchy

public double hierarchy(V v)

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())

Parameters:

v - the vertex whose properties are being measured

Returns:

the hierarchy value for a given vertex

See Also:

localConstraint(Object, Object), aggregateConstraint(Object)

localConstraint

public double localConstraint(V v1,
                              V v2)

Returns the local constraint on 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) ) )^2
 

where

• N(v) = v.getNeighbors()
• p(v,w) = normalized mutual edge weight of v and w

Parameters:

v1 - the first vertex whose local constraint is desired

v2 - the second vertex whose local constraint is desired

Returns:

the local constraint on (v1, v2)

See Also:

normalizedMutualEdgeWeight(Object, Object)

aggregateConstraint

public double aggregateConstraint(V v)

The aggregate constraint on 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)

Parameters:

v - the vertex whose properties are being measured

Returns:

the aggregate constraint on v