BUILT-IN MATHEMATICA SYMBOL

PageRankCentrality

gives a list of page-rank centralities for the vertices in the graph g and weight

.

PageRankCentrality

gives a list of page-rank centralities using weight

and initial centralities

.

MORE INFORMATION

PageRankCentrality gives a list of centralities that satisfy , where is the adjacency matrix of g and is the diagonal matrix consisting of , where is the out-degree of the vertex. »

With a scalar it is taken to mean .

PageRankCentrality is equivalent to PageRankCentrality.

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

EXAMPLES

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Basic Examples (2)

Page-rank centralities for an undirected graph:

With nondefault initial centralities:

Page-rank centralities for a directed graph:

Page-rank centralities for an undirected graph:

In[1]:=

Out[1]=

With nondefault initial centralities:

In[2]:=

Out[2]=

Page-rank centralities for a directed graph:

In[1]:=

Out[1]=

Scope (3)

PageRankCentrality for undirected graphs:

Directed graphs:

Works with large graphs:

Options (3)

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

Specify a higher working precision:

Infinite working precision corresponds to exact computation:

Applications (2)

Highlight the page-rank centrality for CycleGraph:

An unbalanced tree:

Create a directed graph which represents a citation network:

Find the top five most important papers and highlight them:

Properties & Relations (1)

The centrality vector

satisfies the equation

: