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Social Network Analysis, Large-Scale

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

A  network is based on two sets: a set of vertices (nodes), that represent the selected units, and a set of lines (links), thatrepresent ties between units. Each line has two vertices as its end‐points; ifthey are equal it is called a  loop . Vertices and lines forma  graph . A line can be directed – an arc , or undirected – an edge .

Additional data about vertices or lines are usually known – their properties (attributes). Forexample: name/label, type, value, position, … In general

$$ \text{Network $=$ Graph $+$ Data}\:. $$

The data can be measured or computed.

Formally, a network \( {\mathcal{N}=(\mathcal{V},\mathcal{L},\mathcal{P},\mathcal{W}) } \) consists of the following:

  • A graph \( { \mathcal{G}=(\mathcal{V},\mathcal{L}) } \), where \( { \mathcal{V} } \) is the set of vertices and \( { \mathcal{L}=\mathcal{E}\cup\mathcal{A} } \). \( { \mathcal{E}\cap\mathcal{A} = \emptyset } \) is the set of lines. \( { \mathcal{A} } \) is the set of arcs and \( {...

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Abbreviations

Glossary:

For the basic notions on graphs and networks see the Articlea Wouter de Nooy: Social Network Analysis, Graph Theoretical Approaches to.

Network:

consists of vertices linked by lines and additional data about vertices and/or lines.

Network decomposition:

identification of parts of network and their interconnections. Usually it is described by a partition of set of vertices or set of lines.

Time complexity of algorithm:

describes how the time needed to run the algorithm depends on the size of the input data.

Reduction of network:

a network obtained by shrinking each cluster from a given partition into a vertex.

Condensation:

a reduction for strong connectivity partition.

Cut:

a subnetwork of vertices/lines with values of selected property above given threshold.

Island:

a connected subnetwork of selected size of (locally) important, with respect to selected property, vertices/lines.

Pattern searching:

identification of all appearances of selected small subnetwork (pattern or fragment) in a given network.

Topological sort:

procedure to determine a compatible ordering in acyclic network.

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Author information

Authors and Affiliations

  1. University of Ljubljana, Ljubljana, Slovenia

    Vladimir Batagelj

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  1. Vladimir Batagelj
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Batagelj, V. (2009). Social Network Analysis, Large-Scale. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_489

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