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Social Network Visualization, Methods of

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Computational Complexity

Article Outline

Glossary

Definition of the Subject

Introduction

Visualization in Social Network Analysis

Images Based on One Mode Undirected Relations

Images Based on One Mode Directed Relations

Images Based on Two Mode Relations

Images Based on One or Two Mode Data Matrices

Future Directions

Bibliography

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Abbreviations

Adjacent:

A node is adjacent to another if there is an edge connecting them.

Arrow:

A line directed from one node to another.

Binary relation:

A two valued yes/no or on/off relation.

Bipartite graph:

A graph, \( { B = \langle N,E\rangle } \) where N is a finite set of nodes and E is a collection of pairs of nodes in which N is partitioned into two disjoint subsets, N 1 and N 2, and no edge in E has both end points in the same subset.

Blockmodeling:

A procedure for clustering actors such that the actors in each cluster share similar patterns of ties both within and between clusters.

Connected:

Any two nodes in a graph are said to be connected if there is a path from one to the other; a graph is connected if there is a path connecting every pair of nodes.

Cycle:

Any path that begins and ends at the same node.

Digraph:

A directed graph.

Directed graph:

A graph \( { D = \langle N,A\rangle } \) where N is a finite collection of nodes and A is a set of pairs linked by directed lines or arrows.

Directed line:

A line going from a node to another representing a non‐reciprocated link.

Edge:

A line connecting two nodes representing a reciprocated link.

Edge labeled graph:

A graph in which at least two kinds of connections between nodes are identified.

Formal concept analysis:

A method of data analysis based on Galois lattice structure.

Galois lattice:

A dual structure that displays the dependencies of both objects and their properties.

Geodesic:

The shortest path between two nodes.

Graph:

A graph \( { G = \langle N,E\rangle } \) where N is a finite set of nodes and E is a collection of pairs of nodes represented as edges.

Hyperedge:

An edge in a hypergraph that can enclose more than two nodes.

Hypergraph:

A hypergraph, \( { F = \langle N,H\rangle } \), consists of a set of nodes N and a collection of hyperedges, H.

Indegree:

The indegree of a node is the number of directed lines it receives.

Irreflexive:

A relation in which no edge connects any node with itself.

Multidimensional scaling:

A search procedure designed to represent an observed set of proximities or distances in a small number of dimensions.

Node:

A point in a graph.

One mode matrix:

A data matrix in which the rows and columns both represent the same objects.

Outdegree:

The outdegree of a node is the number of directed lines it sends out.

Path:

A path is a sequence of nodes and edges beginning with a node that has an edge connecting it to the next node in the sequence and so on.

Path length:

The length of a path connecting two nodes is the number of edges it contains.

Permutation:

A reordering of the rows, columns, or rows and columns of a matrix.

Principle diagonal:

The set of cells in a square matrix that runs from the upper left to the lower right.

Relation:

A collection of ordered or unordered pairs of nodes.

Singular value decomposition:

an algebraic procedure that decomposes a data matrix into its “basic structure”.

Sociometry:

An early version of social network analysis introduced by Jacob Moreno and Helen Jennings.

Spring embedder:

A kind of multidimensional scaling based on a model in which it is assumed that nodes are connected by springs that pull and push on them.

Symmetric:

A relation in which if a node a is adjacent to another, b, then b is adjacent to a.

Tree:

A graph is a tree if it is connected and contains no cycles.

Two mode matrix:

A data matrix in which the rows and columns represent different objects.

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Author information

Authors and Affiliations

  1. Department of Sociology and Institute for Mathematical Behavioral Science, School of Social Sciences, University of California, Irvine, USA

    Linton C. Freeman

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  1. Linton C. Freeman
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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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Freeman, L.C. (2012). Social Network Visualization, Methods of. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_184

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