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Dynamic Network Visualization: Methods for Meaning with Longitudinal Network Movies.

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### Dynamic Network Visualization:Methods for Meaning with Longitudinal Network Movies.

James Moody, Daniel McFarland, and Skye Bender-deMoll

This work is supported by an NSF Grant (IIS - 0080860 ) awarded to Moody, and a Research Incentive Award provided by Stanford University's Office of Technology and Licensing (Grant #2-CDZ-108) to McFarland. Thanks are extended to participants of James G. March’s Monday Munch at Stanford University and to participants of the Social Structure Research Group at the Ohio State University.

Topic

- Visualizing network dynamics or longitudinal network data
- Importance
- Visualization has always been central to network analysis and is useful for inductive, exploratory research. It has always been used to augment statistical processes and to act as a schematic for qualitative accounts.
- Discussions of network dynamics have lagged in part because there are limited means to visualize network change. The network movies presented in this paper further the discussion of dynamics because space is used to represent movement and social distances over time.
- Catch
- In developing methods of dynamic visualization, we find that our conceptions of relations as static, reified facts has been challenged. What constitutes a tie or social network is thrown into question.
- At what boundary of time can we claim ties exist or not? (Nadel 1955)

To develop dynamic network images, we need to clearly conceptualize how time is encoded in social networks. We conceive of time in two analytically distinct forms: discrete and continuous.

- Discrete renditions of time consist of cross-sectional snapshots of the network. Change is depicted from one network state to another without any (explicit) reference to the sequence of changes that generate change
- Due to research costs and design, most longitudinal network studies use discrete time.
- Continuous renditions of time consist of streaming relational events or interactions recorded with exact starting and ending times. Visual representation of streaming events should unfold as a continuous social process.
- If researchers have panels of network data or continuous representations of network change, they have decisions to make before they represent the data visually.
- What constitutes the network? With discrete waves of sociometric surveys, each wave becomes the networks used in graphic representation. However, with continuous data it becomes more difficult to define a network's temporal boundary (Laumann et al. 1983).
- We propose nominal and realist boundaries of time. (1) Realist notions are those observed and recognized by the individuals of the encounter (e.g. this talk session). (2) Nominalist notions of time-boundaries are defined by the researcher for a variety of theoretical concerns (i.e. development focus, period of historical change, etc).

How to visualize longitudinal network data:

(1) Successive, agglomerating networks (Flipbooks)

- If you have sparse data with discrete notions of time, this form of visualization leaves nodes static, but ghosts old ties and accents new ones.

(2) Successive, non-overlapping windows of time (Movies)

- If you have discrete time data – when you do not know timing and duration beyond a discrete moment, this will show a great deal of change and movement in the graph.
- If you have perfect continuous data – when you have streaming interaction and duration of contact is known, then this is a simple matter of displaying as is second by second (problem – millions of time slices).

(3) Overlapping windows of time (Facilitates stability in movies)

- If you have lots of panels you can assume some lag in relevance. As such, frames can overlap and reduce movement.
- If you have continuous time data, you can create more fine-grained segments of discrete time and assume a level of overlap (McFarland).

Mapping Algorithms Used in Visualizations

Kamada-Kawai

Input matrix: all-pairs-shortest-path

Force model: springs between all pairs which relax to edge length

Optimization: each node has an "energy" according to "spring tension", node with highest energy is moved to optimal position using a Newton-Raphson steepest descent. Energy of network is minimized.

Fruchtermen-Riengold

Input matrix: raw distance matrix

Force model: electrostatic repulsion between all, attraction to connected nodes, force minima is at desired edge length

Optimization: reposition nodes according to the force vector they "feel", the distance nodes are allowed to move is gradually decreased until graph settles.

Moody's Peer-Influence

Input matrix: raw similarity matrix

Model: nodes are repositioned to the weighted average of their peers' coordinates

Optimization: repeated iteration

MDS (metric)

Input matrix: all-pairs-shortest-path matrix or alternate measure of distances/similarities between nodes.

Model: 2D projection of high-dimensional space of the network using matrix algebra (generally SVD) to determine Eigenvectors or principal components which will display a large amount of variance.

Optimization: exact solution

MDS (non-metric)

Input matrix: all-pairs-shortest-path matrix or alternate measure of distances /similarities between nodes

Model: search for a low-stress projection from 2D projection of high-dimensional space of the network

Optimization: there are many different techniques, I don't know enough about them yet.

Agglomerating Coauthor Networks (KK with ghosting and highlights)

- http://www.sociology.ohio-state.edu/jwm/NetMovies/Sub_CD/soc_coath.htm

An animation or interpolation technique is needed to create meaningful movement between temporally adjacent network slices.

- Most useful for this is a sinosodal animation technique that gradually interpolates the position of a node from one resting position to the next.
- Problem: One must assure that the layout at time t+1 is linked to the layout at time t to avoid meaningless movement in the graph. While simple on its face, the separate application of standard layout algorithms to each time slice will rarely give a satisfactory result. Instead, as network layouts usually have no inherent coordinate axes, the entire graph tends to 'rotate' and 'flip' in the display space.
- A partial solution to the problem of spurious movement rests in developing an adequate starting position or "anchor" for the network that results in a meaningful orientation for the graph. The anchor choice is not theoretically neutral and will affect the resulting layout.
- Random starting position (after 1st graph, can result in meaningless movement)
- Constant starting position such as a seating chart (this results in a graph that emphasizes the structure’s central tendency).
- Prior network (t-1) anchor (chaining works best for force-directed layouts – This is what we use in most movies).

SoNIA - Social Network Image AnimatorSoNIA is a Java-based package for visualizing dynamic or longitudinal "network" data. By dynamic, we mean that in addition to information about the relations (ties) between various entities (actors, nodes) there is also information about when these relations occur, or at least the relative order in which they occur. Our intention for SoNIA is to read-in dynamic network information from various formats, aid the user in constructing "meaningful" layouts, and export the resulting images or "movies" of the network, along with information about the techniques and parameter settings used to construct the layouts, and some statistic indicating the "accuracy" or degree of distortion present in the layout.

Two (of three) Studies

- Simulated Balance
- The balance simulation starts with a simple random network of 45 actors who each nominate (on average) 4 other people. At each of 200 iterations, 5 randomly chosen nodes evaluate their local network with respect to transitivity, intransitivity, and reciprocity, and change nominations if doing so increases the comfort of their overall position with respect to these characteristics. Actors favor relations that are transitive, avoid those that are intransitive, seek to reciprocate nominations, and avoid making long-term asymmetric nominations (Gould 2002).
- McFarland Classrooms
- Repeated observations of social interactions in high school classrooms during the 1996-97 school-year. We show dynamic network representations of social interaction from two classes below. The interactions consists of streaming observations of directed conversation turns (of task, social, and negative sanction).

Movie #1Simulation of Balance

Blue = Asymmetric nominations

Green = Symmetric nominations

What’s Gained?

Demonstrates how seemingly stable summary statistics on one network dimension can mask significant structural change on other dimensions, highlighting the holistic-view payoff to this technique.

Example #2: Accelerated Algebra II / Trigonometry

Point – to see shifts in participation structures and process by which coordination and mobilization of students is accomplished.

- What we see are tightly controlled task segments with clear switches and relatively quick adaptation to changes in activities.

Four task segments:

- Maintenance routines (minutes 0-2)
- Recitation on homework problems (min 3-28)

a. More teacher talk and very task-focused.

- Recitation on fun problem (min 29-34)

a. Shift in topic, not really shift in form.

- Group quizzes done in seats (min 35-50)

a. Teacher drops from relevance and stable dyads/triads form.

Movie #2Accelerated Algebra II / Trigonometry

- Kamada-Kawai – 2.5 minute time windows with .5 minute delta (i.e. incremental addition and loss).

For Further Information

- SoNIA software
- http://www.stanford.edu/~skyebend/
- For copies of paper
- http://www.sociology.ohio-state.edu/jwm/NetMovies/Sub_CD/dynamic_nets_public.html
- Where to send comments
- James Moody: moody.77@sociology.osu.edu
- Daniel McFarland: mcfarland@stanford.edu
- Skye Bender-deMoll: skyebend@stanford.edu

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