Encyclopedia of Social Network Analysis and Mining

Living Edition
| Editors: Reda Alhajj, Jon Rokne

Path-Based and Whole-Network Measures

  • Matteo Magnani
  • Moreno Marzolla
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7163-9_241-1

Synonyms

Glossary

Betweenness centrality

A measure of the proportion of shortest paths in a network passing through a specific node or edge.

Closeness centrality

A measure of how close a node is to all the other nodes of a network.

Clustering coefficient

A measure of how much nodes tend to form groups in a network.

Diameter

The maximum distance between two nodes.

Direct connection

An edge between two nodes, usually indicating the existence of a specific relationship, e.g., a friendship between two individuals.

Dyad

A group of two people.

Geodesic distance (or distance)

Length of one of the shortest paths between two nodes.

Indirect connection

A path between two nodes that are not directly connected through an edge.

Node

An entity in a network, usually representing an individual.

Path

A sequence of edges sharing common endpoints. e.g., an edge between ni and nj followed by an edge between nj and nk..

Triangle

Three nodes with an...

Keywords

Undirected Graph Social Network Analysis Cluster Coefficient Betweenness Centrality Geodesic Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

References

  1. Alexanderson GL (2006) About the cover: Euler and Königsberg’s bridges: a historical view. Bull Am Math Soc 43:567–573. doi:10.1090/S0273-0979-06-01130-XCrossRefzbMATHGoogle Scholar
  2. Anthonisse JM (1971) The rush in a directed graph. Technical report BN 9/71, Stichting Mathematisch Centrum, AmsterdamGoogle Scholar
  3. Bacon Oracle (2016) The Oracle of Bacon. https://oracleofbacon.org/. Accessed 11 Nov 2016
  4. Bastian M, Heymann S, Jacomy M (2009) Gephi: an open source software for exploring and manipulating networks. http://www.aaai.org/ocs/index.php/ICWSM/09/paper/view/154
  5. Bearman PS, Moody J, Stovel K (2004) Chains of affection: the structure of adolescent romantic and sexual networks. Am J Sociol 110(1):44–91. doi:10.1086/386272CrossRefGoogle Scholar
  6. Becchetti L, Boldi P, Castillo C, Gionis A (2008) Efficient semi-streaming algorithms for local triangle counting in massive graphs. In: Proceedings of the 14th ACM SIGKDD international conference on knowledge discovery and data mining, KDD ‘08. ACM, New York, pp 16–24. doi:10.1145/1401890.1401898Google Scholar
  7. Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25(2):163–177. doi:10.1080/0022250X.2001.9990249CrossRefzbMATHGoogle Scholar
  8. Brandes U, Pich C (2007) Centrality estimation in large networks. Int J Bifurcation Chaos 17(07):2303–2318. doi:10.1142/S0218127407018403MathSciNetCrossRefzbMATHGoogle Scholar
  9. Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to algorithms, 3rd edn. MIT Press, Cambridge, MAzbMATHGoogle Scholar
  10. Costa LF, Rodrigues FA, Travieso G, Villas Boas PR (2007) Characterization of complex networks: a survey of measurements. Adv Phys 56(1):167–242. doi:10.1080/00018730601170527CrossRefGoogle Scholar
  11. Csardi G, Nepusz T (2006) The igraph software package for complex network research. Inter J Complex Syst 1695. http://igraph.org/
  12. Erdős Number Project (2006) The Erdős number project at Oakland University. https://oakland.edu/enp/. Accessed 26 Nov 2016
  13. Festa P (2006) Shortest path algorithms. In: Resende MGC, Pardalos PM (eds) Handbook of optimization in telecommunications. Springer, New York, pp 185–210. doi:10.1007/978-0-387-30165-5_8CrossRefGoogle Scholar
  14. Floyd RW (1962) Algorithm 97: shortest path. Commun ACM 5(6):345. doi:10.1145/367766.368168CrossRefGoogle Scholar
  15. Fortunato S (2010) Community detection in graphs. Phys Rep 486(3–5):75–174. doi:10.1016/j.physrep.2009.11.002MathSciNetCrossRefGoogle Scholar
  16. Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41. doi:10.2307/3033543CrossRefGoogle Scholar
  17. Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Networks 1(3):215–239. doi:10.1016/0378-8733(78)90021-7CrossRefGoogle Scholar
  18. Goncalves B, Perra N, Vespignani A (2011) Modeling users’ activity on twitter networks: validation of Dunbar’s number. PLoS ONE 6(8):e22656. doi:10.1371/journal.pone.0022656CrossRefGoogle Scholar
  19. Guha S, McGregor A (2012) Graph synopses, sketches, and streams: a survey. Proc VLDB Endow 5(12):2030–2031. doi:10.14778/2367502.2367570CrossRefGoogle Scholar
  20. Harary F (1969) Graph theory. Addison-Wesley, ReadingzbMATHGoogle Scholar
  21. Harary F, Norman RZ (1953) Graph theory as a mathematical model in the social sciences. Institute for Social Research, University of Michigan, Ann ArborGoogle Scholar
  22. Johnson DB (1977) Efficient algorithms for shortest paths in sparse networks. J ACM 24(1):1–13. doi:10.1145/321992.321993MathSciNetCrossRefzbMATHGoogle Scholar
  23. Lambertini M, Magnani M, Marzolla M, Montesi D, Paolino C (2014) Large-scale social network analysis. In: Gkoulalas-Divanis A, Labbi A (eds) Large-scale data analytics. Springer, New York, pp 155–187. doi:10.1007/978-1-4614-9242-9 6CrossRefGoogle Scholar
  24. Latapy M (2008) Main-memory triangle computations for very large (sparse (power-law)) graphs. Theor Comput Sci 407(1):458–473. doi:10.1016/j.tcs.2008.07.017MathSciNetCrossRefzbMATHGoogle Scholar
  25. Latora V, Marchiori M (2001) Efficient behavior of small-world networks. Phys Rev Lett 87:198,701. doi:10.1103/PhysRevLett.87.198701CrossRefGoogle Scholar
  26. Latora V, Marchiori M (2004) How the science of complex networks can help developing strategies against terrorism. Chaos, Solitons Fractals 20(1):69–75. doi:10.1016/S0960-0779(03) 00429-6CrossRefzbMATHGoogle Scholar
  27. Leskoveč J, Sosiˇč R (2016) Snap: a general-purpose network analysis and graph-mining library. ACM Trans Intell Syst Technol 8(1):20. doi:10.1145/2898361Google Scholar
  28. Luce R, Perry A (1949) A method of matrix analysis of group structure. Psychometrika 14:95–116. doi:10.1007/BF02289146MathSciNetCrossRefGoogle Scholar
  29. Lumsdaine A, Gregor D, Hendrickson B, Berry JW (2007) Challenges in parallel graph processing. Parallel Process Lett 17(1):5–20. doi:10.1142/S0129626407002843MathSciNetCrossRefGoogle Scholar
  30. Lusseau D (2003) The emergent properties of a dolphin social network. Proc R Soc Lond B Biol Sci 270(Suppl 2):S186–S188. doi:10.1098/rsbl.2003.0057CrossRefGoogle Scholar
  31. McCormick TH, Salganik MJ, Zheng T (2010) How many people do you know?: efficiently estimating personal network size. J Am Stat Assoc 105(489):59–70. doi:10.1198/jasa.2009.ap08518MathSciNetCrossRefzbMATHGoogle Scholar
  32. Moreno JL (1934) Who shall survive? A new approach to the problem of human Interrelations. Nervous and Mental Disease Publishing Co., Washington, DCCrossRefGoogle Scholar
  33. Newman MEJ (2001) The structure of scientific collaboration networks. Proc Natl Acad Sci U S A 98(2):404–409. doi:10.1073/pnas.98.2.404MathSciNetCrossRefzbMATHGoogle Scholar
  34. Newman MEJ (2005) A measure of betweenness centrality based on random walks. Soc Networks 27(1):39–54. doi:10.1016/j.socnet.2004.11.009MathSciNetCrossRefGoogle Scholar
  35. Newman MEJ (2010) Networks: an introduction. Oxford University Press, OxfordCrossRefzbMATHGoogle Scholar
  36. NodeXL (2012) Nodexl, a graph visualization and manipulation software. http://nodexl.codeplex.com. Accessed 6 Dec 2016
  37. Opsahl T, Panzarasa P (2009) Clustering in weighted networks. Soc Networks 31(2):155–163. doi:10.1016/j.socnet.2009.02.002CrossRefGoogle Scholar
  38. Opsahl T, Agneessens F, Skvoretz J (2010) Node centrality in weighted networks: generalizing degree and shortest paths. Soc Networks 32(3):245–251. doi:10.1016/j.socnet.2010.03.006CrossRefGoogle Scholar
  39. Peay ER (1980) Connectedness in a general model for valued networks. Soc Networks 2(4):385–410. doi:10.1016/0378-8733(80)90005-2MathSciNetCrossRefGoogle Scholar
  40. R Core Team (2012) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org. ISBN:3-900051-07-0
  41. Rossi L, Magnani M (2012) Conversation practices and network structure in twitter. https://www.aaai.org/ocs/index.php/ICWSM/ICWSM12/paper/view/4634
  42. Sabidussi G (1966) The centrality index of a graph. Psychometrika 31(4):581–603. doi:10.1007/ BF02289527MathSciNetCrossRefzbMATHGoogle Scholar
  43. Wang Y, Davidson A, Pan Y, Wu Y, Riffel A, Owens JD (2016) Gunrock: a high-performance graph processing library on the GPU. In: Proceedings of 21st ACM SIGPLAN symposium on principles and practice of parallel programming, PPoPP ‘16. ACM, New York, pp 11:1–11:12. doi:10.1145/2851141.2851145Google Scholar
  44. Wasserman S, Faust K (1994) Social network analysis. Cambridge University Press, New YorkCrossRefzbMATHGoogle Scholar
  45. Watts DJ, Strogatz SH (1998) Collective dynamics of “small-world” networks. Nature 393:440–442. doi:10.1038/30918CrossRefGoogle Scholar
  46. White DR, Borgatti SP (1994) Betweenness centrality measures for directed graphs. Soc Networks 16(4):335–346. doi:10.1016/0378-8733(94)90015-9CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2016

Authors and Affiliations

  1. 1.Department of Information TechnologyUppsala UniversityUppsalaSweden
  2. 2.Department of Computer Science and EngineeringUniversity of BolognaBolognaItaly

Section editors and affiliations

  • Przemysław Kazienko
    • 1
  • Jaroslaw Jankowski
    • 2
  1. 1.Department of Computer Science and Management, Institute of InformaticsWrocław University of TechnologyWrocławPoland
  2. 2.Faculty of Computer Science and Information TechnologyWest Pomeranian University of TechnologySzczecinPoland