BUILT-IN MATHEMATICA SYMBOL

KatzCentrality

gives a list of Katz centralities for the vertices in the graph g and weight

.

KatzCentrality

gives a list of Katz centralities using weight

and initial centralities

.

MORE INFORMATION

KatzCentrality gives a list of centralities that satisfy , where is the adjacency matrix of g.

With a scalar, it is taken to mean .

KatzCentrality is equivalent to KatzCentrality.

With and where is the largest eigenvalue of , KatzCentrality is equivalent to EigenvectorCentrality.

With , the centralities are all given by .

The option WorkingPrecision->p can be used to control the precision used in internal computations.

EXAMPLES

CLOSE ALL

Basic Examples (2)

Katz centralities for an undirected graph:

With nondefault initial centralities:

Katz centralities for a directed graph:

Katz centralities for an undirected graph:

In[1]:=

In[2]:=

Out[2]=

With nondefault initial centralities:

In[3]:=

Out[3]=

Katz centralities for a directed graph:

In[1]:=

Out[1]=

Scope (3)

KatzCentrality for undirected graphs:

Directed graphs:

Works with large graphs:

Options (3)

By default, KatzCentrality finds centralities using machine-precision computations:

Specify a higher working precision:

Infinite working precision corresponds to exact computation:

Applications (2)

Highlight the Katz centrality for CycleGraph:

An unbalanced tree:

Create a directed graph that represents a citation network:

Find the top 5 most important papers and highlight them:

Properties & Relations (3)

The centrality vector

satisfies the equation

:

EigenvectorCentrality is a special case of KatzCentrality:

Use

as the parameter for KatzCentrality:

As

all vertices get the same centrality: