Article Outline
Glossary
Definition of the Subject
Introduction
Basic Concepts
Two-Mode Data in Social Network Analysis
Unimodal Approaches to Two-Mode Data
Bimodal Approaches to Two-Mode Data
Conclusion
Future Directions
Bibliography
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Notes
- 1.
For directed graphs, we require \( { C(N^{o}(u)) = C(N^{o}(v)) } \) and \( { C(N^{i}(u)) = C(N^{i}(v)) } \), where \( { N^{o}(v) } \) refers to the set of nodes that v sends a tie to, and \( { N^{i}(u) } \) refers to the set of nodes that v receives a tie from.
Abbreviations
- 2-Mode matrix:
-
A (2‑dimensional) matrix is said to be 2‑mode if the rows and columns index different sets of entities (e. g., the rows might correspond to persons while the columns correspond to organizations). In contrast, a matrix is 1‑mode if the rows and columns refer to the same set of entities, such as a city‐by‐city matrix of distances.
- Blockmodel:
-
A blockmodel is a partitioning of the cells of a matrix into blocks that is induced by the partitioning the rows and columns into classes and sorting the matrix such that rows (and columns) that belong to the same class are next to each other. More specifically, two matrix cells x i j and x m p are in the same block if \( { \text{class}(i) = \text{class}(m) } \) and \( { \text{class}(j) = \text{class}(p) } \).
- Centrality:
-
A family of concepts for characterizing the structural importance of a node's position in a network.
- Graph cohesion:
-
A family of concepts characterizing the extent of connectedness of a graph, such as density (the proportion of pairs of nodes that have ties with each other), or average path distance.
- Multidimensional scaling (MDS):
-
A method of locating points in space such that Euclidean distances between the points correspond to a matrix of input similarities/distances among objects. Used to provide visual representations of 1‑mode matrices such as correlation matrices or perceptual distances among objects.
- Regular equivalence:
-
The definition of regular equivalence is recursive. If two nodes are regularly equivalent, then they are connected to regularly equivalent nodes.Regular equivalence is used to identify nodes that are playing the same structural role, even if they are not connected to each other.
- Social network (or, in graph theory, a graph):
-
A collection of nodes (also referred to as vertices or actors) together with a set of ties (also known as edges or links) that connect pairs of nodes. Typically used to represent social relations such as who is friends with whom, or who is the supervisor of whom.
- Structural equivalence:
-
At an intuitive level, a pair of nodes is said to be structurally equivalent to the extent that they occupy identical locations in a network, meaning that they are connected to exactly the same others. Structurally equivalent nodes are identical with respect to all structural properties, such as centrality or subgroup membership.
Bibliography
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Borgatti, S.P. (2012). Social Network Analysis, Two-Mode Concepts in. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_179
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