Title: | Link Prediction Methods |
---|---|
Description: | Implementations of most of the existing proximity-based methods of link prediction in graphs. Among the 20 implemented methods are e.g.: Adamic L. and Adar E. (2003) <doi:10.1016/S0378-8733(03)00009-1>, Leicht E., Holme P., Newman M. (2006) <doi:10.1103/PhysRevE.73.026120>, Zhou T. and Zhang Y (2009) <doi:10.1140/epjb/e2009-00335-8>, and Fouss F., Pirotte A., Renders J., and Saerens M. (2007) <doi:10.1109/TKDE.2007.46>. |
Authors: | Michal Bojanowski [aut, cre] , Bartosz Chrol [aut], National Science Centre [fnd] (grant 2012/07/D/HS6/01971) |
Maintainer: | Michal Bojanowski <[email protected]> |
License: | MIT + file LICENSE |
Version: | 1.0-1 |
Built: | 2024-10-09 02:58:24 UTC |
Source: | https://github.com/recon-icm/linkprediction |
Implements most of existing methods proximity-based methods of link
prediction in graphs. See proxfun
.
Authors thank (Polish) National Science Centre for support through SONATA grant 2012/07/D/HS6/01971 for the project Dynamics of Competition and Collaboration in Science: Individual Strategies, Collaboration Networks, and Organizational Hierarchies (recon.icm.edu.pl).
General function for calculating several types of vertex proximities in a graph.
proxfun(graph, ...) ## S3 method for class 'igraph' proxfun( graph, method, v1 = NULL, v2 = v1, value = c("matrix", "edgelist", "graph"), ... ) ## S3 method for class 'network' proxfun( graph, method, v1 = NULL, v2 = v1, value = c("matrix", "edgelist", "graph"), ... )
proxfun(graph, ...) ## S3 method for class 'igraph' proxfun( graph, method, v1 = NULL, v2 = v1, value = c("matrix", "edgelist", "graph"), ... ) ## S3 method for class 'network' proxfun( graph, method, v1 = NULL, v2 = v1, value = c("matrix", "edgelist", "graph"), ... )
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 .
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 integer
node IDs. If value = "edgelist"
a data.frame
with three
columns:
ID of a start node of an edge
ID of an end node of an edge
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.
if(requireNamespace("igraph")) { g <- igraph::make_graph(~ A -- C:D:E -- B -- F -- G:H -- I) # Adamic-Adar proxfun(g, method="aa", value="edgelist") # Random Walk with Restart proxfun(g, method="rwr", value="edgelist") }
if(requireNamespace("igraph")) { g <- igraph::make_graph(~ A -- C:D:E -- B -- F -- G:H -- I) # Adamic-Adar proxfun(g, method="aa", value="edgelist") # Random Walk with Restart proxfun(g, method="rwr", value="edgelist") }
Giant component of University of Warsaw (UW) co-authorship network based on publications from years 2007-2009 (period 1) and 2010-2012 (period 2).
An igraph
object with undirected graph with 1486 vertices and 7505 edges, and the following attributes:
affiliation
– Vertex attribute identifying groups of departments:
natural sciences, social sciences, humanities, other (other departments of
UW), and external (co-authors who are not employees of UW)
color
, size
, label
– Vertex attributes for easy plotting. Color corresponds
to the affiliation
attribute.
p1
– Logical edge attribute. It is TRUE
if researchers incident on
that edge co-authored at least one publication in period 1.
p2
– Logical edge attribute. It is TRUE
if researchers incident on
that edge co-authored at least one publication in period 2.
The basis of this network is a co-authorship graph built from all articles, books, and chapters in edited volumes published in years 2007-2012 that have at least one employee of University of Warsaw as a (co)author.
Polish Scholarly Bibliography https://pbn.nauka.gov.pl.
# Plot it data(uw) set.seed(666) xy <- igraph::layout_with_fr(uw) plot(uw, layout=xy, vertex.frame.color=par("bg")) legend( "topright", title = "Affiliation", legend = unique(igraph::V(uw)$affiliation), pt.bg = unique(igraph::V(uw)$color), pch = 21, bty = "n" )
# Plot it data(uw) set.seed(666) xy <- igraph::layout_with_fr(uw) plot(uw, layout=xy, vertex.frame.color=par("bg")) legend( "topright", title = "Affiliation", legend = unique(igraph::V(uw)$affiliation), pt.bg = unique(igraph::V(uw)$color), pch = 21, bty = "n" )