Networks

Lincoln Mullen

http://lincolnmullen.com

What are networks used for?

Newspaper reprints

Ryan Cordell, David Smith, et al., Network of Viral Text Sharing, 1836-1860, Viral Texts.
Ryan Cordell, David Smith, et al., “Network of ‘Viral Text’ Sharing, 1836-1860,” Viral Texts.

Correspondence networks

Correspondence of Locke (blue) and Voltaire (yellow), Mapping the Republic of Letters.
Correspondence of Locke (blue) and Voltaire (yellow), Mapping the Republic of Letters.

Membership in organizations

George Oberle, networks of learned organizations in the early republic.
George Oberle, networks of learned organizations in the early republic.

Co-citation networks

Kieran Healy, detail of A Co-Citation Network for Philosophy
Kieran Healy, detail of “A Co-Citation Network for Philosophy

Transportation networks

Washington, DC, Metro map
Washington, DC, Metro map

Transportation networks

Walter Scheidel and Elijah Meeks, Orbis: The Stanford Geospatial Network Model of the Roman World.
Walter Scheidel and Elijah Meeks, Orbis: The Stanford Geospatial Network Model of the Roman World.

Exercise

Working with a partner, try to answer these questions:

  • What would a network visualization in your domain look like?
  • Draw up a list of the kinds of data you would need?
  • What would be the source for that data?
  • Can you create a sketch of the network data?
  • What kinds of questions would it answer?

What is a network?

Network = graph

What humanities scholars call a network, mathematicians call a graph.

A graph is defined as

  • a set of nodes (or vertices) and
  • a set of edges that connect those edges.

Nodes and edges

What do the nodes and edges mean?

Nodes Edges
People Letters
People Membership
Organization People
Publications Citations
Cities Roads/canals/railways
Cities Imports/exports
Documents Text borrowing
Organizations Money

Directed versus undirected

What does the data look like?

nodes
names size color
A 19 green
B 19 green
C 19 red
D 27 red
E 11 green
F 18 green
Edges
node1 node2 weight
A B 5
B C 3
D B 8
D C 6
D E 4
F D 4

Adjacency matrix: an alternative form

## 6 x 6 sparse Matrix of class "dgCMatrix"
##   A B C D E F
## A . 5 . . . .
## B . . 3 8 . .
## C . . . 6 . .
## D . . . . 4 4
## E . . . . . .
## F . . . . . .

Exercise: What does the data look like?

Kellen Funk and Lincoln Mullen, work in progress on state-to-state borrowings in codes of civil procedure.
Kellen Funk and Lincoln Mullen, work in progress on state-to-state borrowings in codes of civil procedure.

How do we interpret a network?

Problems

  • Networks are often incomplete (for example, ego networks).
  • Networks are extremely difficult to visualize.
  • Networks are hard to scale.
  • Layouts are imposed, not inherent. Graphs can be topologically similar but layout entirely different

All these graphs are identical

Still identical

And still identical

Measures of networks

  • Degree: how many edges does a node have? (Or, how many neighbors does a node have?)
  • In-degree/out-degree: takes into account directionality
  • Strength/weighted degree: degree taking into accounts weights of edges
  • Betweenness centrality: nodes that could be hubs
  • Closeness centrality: center of the graph
  • Eigenvector centrality: nodes connected to central nodes (e.g., page rank)
  • Modularity/community detection: groups of similar nodes

Bipartite networks

Bipartite networks

  • Bipartite networks have two kinds of nodes.
  • Examples: members in organizations
  • Bipartite networks can be projected into unipartite networks with only one type of node
  • Each bipartite network will have two projections, one for each type of node.

Bipartite: members and organizations

Bipartite projected to students

Bipartite projected to courses

Application

Exercise

Working in a group, create a network visualization using one of the provided datasets. Start by changing these properties:

  • Layout
  • Node size
  • Node color according to modularity
  • Labels