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2012 | OriginalPaper | Buchkapitel

5. Metrics and Models for Social Networks

verfasst von : Nicolás Ignacio Bersano-Méndez, Satu Elisa Schaeffer, Javier Bustos-Jiménez

Erschienen in: Computational Social Networks

Verlag: Springer London

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Abstract

Social networks can be modeled and analyzed in terms of graph theory. This chapter provides an overview of the mathematical modeling of social networks with an overview of the metrics used to characterize them and the models used to artificially mimic the formation of such networks. We discuss metrics based on distances, degrees, and neighborhoods as well as the use of such metrics to detect change in the network structure. We also discuss the kind of structural differences that distinguish social networks from other types of natural networks together with the implications of these differences about the way in which these networks function.

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Fußnoten
1
Another possible visualization (cf. [19]) is using a line that is thicker at the source and gradually becomes thinner before reaching the target vertex.
 
2
In general graph theory, also edges from a vertex to itself (called loops or reflexive edges) are of interest, but these are not usually present in graphs that represent social networks.
 
3
Whereas the number of vertices is called the order of the graph, the number of edges is often called its size.
 
4
The binomial coefficient is \(\left ({ n \atop k} \right ) = \frac{n!} {k!(n-k)!}\), where k!  = 1 ⋅2 ⋅(n − 1) ⋅n is the factorial.
 
5
A complete graph is one where all vertices are neighbors among themselves, that is, all possible edges are present.
 
6
A vertex set S ⊆ V is an independent set in G = (V, E) if none of its member vertices are adjacent in E.
 
7
A queue is a data structure where incoming data is appended at the end and removals are only done in the beginning of the structure.
 
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Metadaten
Titel
Metrics and Models for Social Networks
verfasst von
Nicolás Ignacio Bersano-Méndez
Satu Elisa Schaeffer
Javier Bustos-Jiménez
Copyright-Jahr
2012
Verlag
Springer London
DOI
https://doi.org/10.1007/978-1-4471-4048-1_5

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