Encyclopedia of Social Network Analysis and Mining

2014 Edition
| Editors: Reda Alhajj, Jon Rokne

Path-Based and Whole-Network Measures

  • Matteo Magnani
  • Moreno Marzolla
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-6170-8_241



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


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


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


An entity in a network, usually representing an individual


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


Three nodes with an edge...

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  1. Anthonisse JM (1971) The rush in a directed graph. Technical report BN 9/71, Stichting Mathematisch Centrum, AmsterdamGoogle Scholar
  2. 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
  3. Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25(2):163–177. doi: 10.1080/0022250X.2001.9990249zbMATHGoogle Scholar
  4. Brandes U, Pich C (2007) Centrality estimation in large networks. Int J Bifurc Chaos 17(07):2303–2318. doi:10.1142/S0218127407018403zbMATHMathSciNetGoogle Scholar
  5. Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to algorithms, 3rd edn. MIT, CambridgezbMATHGoogle Scholar
  6. Costa LDF, Rodrigues FA, Travieso G, Villas Boas PR (2007) Characterization of complex networks: a survey of measurements. Adv Phys 56(1):167–242. doi: 10.1080/00018730601170527Google Scholar
  7. 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_8Google Scholar
  8. Floyd RW (1962) Algorithm 97: shortest path. Commun ACM 5(6):345. doi:10.1145/367766.368168Google Scholar
  9. Fortunato S (2010) Community detection in graphs. Phys Rep 486(3–5):75–174. doi:10.1016/ j.physrep.2009.11.002MathSciNetGoogle Scholar
  10. Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41Google Scholar
  11. Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Netw 1(3):215–239. doi:10.1016/0378–8733(78)90021–7MathSciNetGoogle Scholar
  12. Gephi (2012) Gephi, an open source graph visualization and manipulation software. http://www.gephi.org/, version 0.8.1-beta, released on 29 Mar 2012
  13. 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.0022656Google Scholar
  14. Guha S, McGregor A (2012) Graph synopses, sketches, and streams: a survey. PVLDB 5(12):2030–2031Google Scholar
  15. Harary F (1969) Graph theory. Addison-Wesley, Reading, MAGoogle Scholar
  16. 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
  17. IGraph (2012) The igraph library for complex network research. http://igraph.sourceforge.net/, version 0.6, released on 11 June 2012
  18. Johnson DB (1977) Efficient algorithms for shortest paths in sparse networks. J ACM 24(1): 1–13. doi: 10.1145/321992.321993zbMATHGoogle Scholar
  19. Lambertini M, Magnani M, Marzolla M, Montesi D, Paolino C (2014) Large scale social network analysis. Large-scale data analytics. Springer, New YorkGoogle Scholar
  20. Latapy M (2008) Main-memory triangle computations for very large (sparse (power-law)) graphs. Theor Comput Sci 407(1–3):458–473. doi:10.1016/j.tcs.2008.07.017zbMATHMathSciNetGoogle Scholar
  21. Latora V, Marchiori M (2001) Efficient behavior of small- world networks. Phys Rev Lett 87(19): 198701Google Scholar
  22. Luce R, Perry A (1949) A method of matrix analysis of group structure. Psychometrika 14:95–116. doi:10.1007/BF02289146MathSciNetGoogle Scholar
  23. Lumsdaine A, Gregor D, Hendrickson B, Berry JW (2007) Challenges in parallel graph processing. Parallel Process Lett 17(1):5–20MathSciNetGoogle Scholar
  24. Newman MEJ (2005) A measure of betweenness centrality based on random walks. Soc Netw (27):39–54Google Scholar
  25. Newman MEJ (2010) Networks: an introduction. Oxford University Press, OxfordGoogle Scholar
  26. NodeXL (2012) Nodexl, a graph visualization and manipulation software. http://nodexl.codeplex.com, version
  27. Opsahl T, Panzarasa P (2009) Clustering in weighted networks. Soc Netw 31(2): 155—163. doi:10.1016/j.socnet.2009.02.002Google Scholar
  28. Opsahl T, Agneessens F, Skvoretz J (2010) Node centrality in weighted networks: generalizing degree and shortest paths. Soc Netw 32(3):245–251. doi:10.1016/j.socnet.2010.03.006Google Scholar
  29. Peay ER (1980) Connectedness in a general model for valued networks. Soc Netw 2(4):385–410. doi: 10.1016/0378–8733(80)90005–2MathSciNetGoogle Scholar
  30. 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
  31. Rossi L, Magnani M (2012) Conversation practices and network structure in twitter. In: ICWSM, DublinGoogle Scholar
  32. Sabidussi G (1966) The centrality index of a graph. Psychometrika 31:581–603. doi:10.1007/BF02289527zbMATHMathSciNetGoogle Scholar
  33. SNAP (2011) Stanford network analysis project network analysis library. http://snap.stanford.edu/snap, version 2011–12-31
  34. Wasserman S, Faust K (1994) Social network analysis. Cambridge University Press, CambridgeGoogle Scholar
  35. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442. doi:10.1038/30918Google Scholar
  36. White DR, Borgatti SP (1994) Betweenness centrality measures for directed graphs. Soc Netw 16(4): 335–346Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Matteo Magnani
    • 1
  • Moreno Marzolla
    • 2
  1. 1.Computing Science Division, Uppsala UniversityUppsalaSweden
  2. 2.Department of Computer Science and Engineering, University of BolognaBolognaItaly