Description Usage Arguments Details Value References Examples

General function for calculating several types of vertex proximities in a graph.

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`graph` |
an object of class |

`...` |
additional arguments specific for a selected measure |

`method` |
single character, the method to be used, see Details |

`v1, v2` |
vectors of vertices between which similarity will be calculated. Character vector is interpreted as vertex names. Numeric vector as vertex ids. |

`value` |
a character string giving a type of the object that should be
returned. This must be one of " |

This function calculates vertex proximities in graph `graph`

with the
selected `method`

. The `graph`

has to be undirected and connected.
Some of the methods support computation only for selected vertices, which
should be more efficient when needed. Supplying vertex IDs or names (if
present in the `graph`

) to `v1`

and `v2`

will calculate
proximities of *v1 x v2*.

The following `method`

s are available (see ```
vignette("proxfun",
package="linkprediction")
```

for more details and formal definitions):

`aa`

Adamic-Adar index (Adamic and Adar 2001). Additional arguments are passed to igraph::similarity.

`act`

Average Commute Time (Fouss, Pirotte, Renders, and Saerens 2007)

`act_n`

Normalized Average Commute Time (Fouss et al. 2007)

`cn`

Common Neighbours

`cos`

Cosine similarity (Salton and McGill 1986)

`cos_l`

cosine similarity on L+ (Fouss et al. 2007)

`dist`

graph distance

`hdi`

Hub Depressed Index (Ravasz, Somera, Mongru, Oltvai, and Barabasi 2002)

`hpi`

Hub Promoted Index (Ravasz et al. 2002)

`jaccard`

Jaccard coefficient (Jaccard 1912)

`katz`

Katz index (Katz 1953)

`l`

L+ directly (Fouss et al. 2007)

`lhn_local`

Leicht-Holme-Newman Index (Leicht, Holme, and Newman 2006)

`lhn_global`

Leicht-Holme-Newman Index global version (Leicht et al. 2006)

`lp`

Local Path Index (Zhou, Lu, and Zhang 2009)

`mf`

Matrix Forest Index (Chebotarev P. Yu. 1997)

`pa`

preferential attachment (Barabasi and Albert 1999)

`ra`

resource allocation (Zhou et al. 2009)

`rwr`

random walk with restart (Brin and Page 1998). Additional argument

`alpha`

(default value 0.3) is the probability that the walk will restart after a step.`sor`

sorensen index/dice coefficient (Sorensen 1948)

If `value = "matrix"`

a matrix with `length(v1)`

rows and
`length(v2)`

with `rownames`

and `colnames`

equal to `v1`

and `v2`

respectively. If `value = "edgelist"`

a `data.frame`

with three columns:

- from
ID of a start node of an edge

- to
ID of an end node of an edge

- value
similarity score for that edge

Edges with similarity score 0 are omitted. If `value = "graph"`

an
object of class `igraph`

or `network`

, depending on the class of
input graph. Returned graph has the same structure (graph and node
attributes, etc.) as the input graph, except for edges - original edges are
skipped, and new edges with positive similarity score are added. Edged
attribute "weight" indicates similarity score.

Adamic L and Adar E (2003). "Friends and Neighbors on the Web." *Social Networks*, *25*,
pp. 211-230 doi: 10.1016/S0378-8733(03)00009-1.

Barabasi A and Albert R (1999). "Emergence of Scaling in Random Networks." *Science*,
*286*(5439), pp. 509-512.

Brin S and Page L (1998). "The anatomy of a large-scale hypertextual Web search engine ."
_Computer Networks and ISDN Systems _, *30*(1-7), pp. 107 - 117. Proceedings of the
Seventh International World Wide Web Conference .

Chebotarev P. Yu. SEV (1997). "The matrix-forest theorem and measuring relations in small
social groups ." _Automation and Remote Control _, *58*(9), pp. 1505-1514.

Fouss F, Pirotte A, Renders J and Saerens M (2007). "Random-Walk Computation of
Similarities Between Nodes of a Graph with Application to Collaborative Recommendation."
*IEEE Transactions on Knowledge and Data Engineering*, *19*(3), pp. 355-369 doi: 10.1109/TKDE.2007.46.

Jaccard P (1912). "The Distribution of the Flora in the Alpine Zone 1" *New
Phytologist*, *11*(2), pp. 37-50.

Katz L (1953). "A new status index derived from sociometric analysis." *Psychometrika*,
*18*(1), pp. 39-43.

Leicht EA, Holme P and Newman MEJ (2006). "Vertex similarity in networks." *Phys. Rev.
E*, *73*(2), pp. 026120 doi: 10.1103/PhysRevE.73.026120.

Ravasz E, Somera AL, Mongru DA, Oltvai ZN and Barabasi A (2002). "Hierarchical
Organization of Modularity in Metabolic Networks." *Science*, *297*(5586), pp. 1551-1555.

Salton G and McGill MJ (1986). *Introduction to Modern Information Retrieval*.
McGraw-Hill, Inc., New York, NY, USA.

Sorensen T (1948). "A Method of Establishing Groups of Equal Amplitude in Plant Sociology
Based on Similarity of Species Content and Its Application to Analyses of the Vegetation
on Danish Commons." *Biologiske Skrifter*, *5*, pp. 1-34.

Zhou T, Lu L and Zhang Y (2009). "Predicting missing links via local information." *The
European Physical Journal B*, *71*(4), pp. 623-630 doi: 10.1140/epjb/e2009-00335-8.

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