General function for calculating several types of vertex proximities in a graph.
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an object of class
additional arguments specific for a selected measure
single character, the method to be used, see Details
vectors of vertices between which similarity will be calculated. Character vector is interpreted as vertex names. Numeric vector as vertex ids.
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
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
v2 will calculate
proximities of v1 x v2.
methods are available (see
package="linkprediction") for more details and formal definitions):
Adamic-Adar index (Adamic and Adar 2001). Additional arguments are passed to igraph::similarity.
Average Commute Time (Fouss, Pirotte, Renders, and Saerens 2007)
Normalized Average Commute Time (Fouss et al. 2007)
Cosine similarity (Salton and McGill 1986)
cosine similarity on L+ (Fouss et al. 2007)
Hub Depressed Index (Ravasz, Somera, Mongru, Oltvai, and Barabasi 2002)
Hub Promoted Index (Ravasz et al. 2002)
Jaccard coefficient (Jaccard 1912)
Katz index (Katz 1953)
L+ directly (Fouss et al. 2007)
Leicht-Holme-Newman Index (Leicht, Holme, and Newman 2006)
Leicht-Holme-Newman Index global version (Leicht et al. 2006)
Local Path Index (Zhou, Lu, and Zhang 2009)
Matrix Forest Index (Chebotarev P. Yu. 1997)
preferential attachment (Barabasi and Albert 1999)
resource allocation (Zhou et al. 2009)
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.
sorensen index/dice coefficient (Sorensen 1948)
value = "matrix" a matrix with
length(v1) rows and
colnames equal to
v2 respectively. If
value = "edgelist" a
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
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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