Approaches to the analysis and visualization of multi-modal and multi-relational networks

Overview TERMINOLOGY ISSUES (generic tasks) EXAMPLE TASKS and APPROACHES REFERENCES

Terminology Multi-relational (MR) Multimodal (MM) – composed on 2+ node types Bipartite - … and only of links between types – hence tripartite, s-/k-partite In the real world, MMMR is common!

ISSUES (generic tasks) Lingua franca – graph theory (limitations when applied to transport) Partitioning problem (maxflow/mincut) Temporal modeling of n-mode network interactions Centrality analysis with n-mode data (even bipartite) Blockmodelling (categorization of nodes by structural equivalence) Detecting anomalous differences between multiple relations – E.g. a Process model (or hierarchy) vs. a matrix of observed communication Semantics of nodes – how to translate data into an ontology? Impacts of disruption – e.g. predicting transfer of ‘flow’ between networks, making quantified predictions of delay Single visualizations vs. multiple interacting visualizations

Example: Davis’ original (hand-crafted)

Spring embedder

Example: Davis (spring/eyeball)

Gower

Principal Components

Layered (apologies)

Trad approach to bipartite SN data Create secondary matrices: – row overlap (people attending the same meeting) – column overlap (meetings attended by same person) Analyse positions, groups, centrality in these Problem: ‘false groups’

False groups 2 of 2-mode, bipartite 1-mode (rows)

Contour map comparison Community nesting, groups by KCommunity nesting, groups by I

Problems and approaches

Galois Lattice

Useful references Fararo, T J., and P. Doreian. (1984). "Tripartite Structural Analysis: Generalizing the Breiger-Wilson Formalism." Social Networks, 6, Freeman, L. (1996) Cliques, Galois lattices, and the structure of human social groups, Social Networks, 18 (3), CASOS’ metamatrix approach (

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