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Network Frontiers &

open Problems

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Open Issues & Future Directions

  1. Data: So much data, so little time.

Many sorts of new network data. What do we do with it?

    • Scaling up. Really Big data – O(M) or O(B) nodes/edges.

      • Scale Theory, Models will follow
      • Divide & Conquer
      • Statistical models?

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Open Issues & Future Directions

2. Going Deep. Real-time traces produce micro-level data that are “deep” even on small populations. How do we deal with this?

      • Networks Are in Our Heads, but Our Heads Are Networked
        1. Are We Living the Same Network? Cognitive social structures.
        2. Individual Processes. Not all networks are networks.
        3. Dyadic Processes. What do we know about the micro foundations of specific relations?
        4. Small Group Processes. What do we know about the lived dynamics of specific types of groups?

Good places for ethnographic depth.

      • Going Deeper into Diffusion: Does the Trip Change the Traveler? Do the Drivers Pave the Road?
        1. Information flows change the network
        2. Actors identities distort information as it flows
        3. Socially relevant information needs to be continuously refreshed to become institutionalized

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Open Issues & Future Directions

3. Comparing Structures in the Middle. We need studies of the “middle range” that allow us to compare across networks.

      • Add Health 🡪 271 replications
      • Prosper 🡪 360(ish) classrooms
      • Christakis et al🡪 80 Honduran Villages
      • Mohanan et al (in progress) 🡪 75 Indian Villages.

      • Poverty of Riches? Finding Structural Patterns across Multiple Networks
      • Links across Relations: From Multiplexity to Multilayer Networks
      • Field Experiments and Quasi-Experiments with Multiple Networks

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  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

Detailed issues JWM would like to see folks work on.

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Open Problems

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

Edge timing has profound effects on discrete transmission dynamics

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions

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Open Problems

Edge timing has profound effects on discrete transmission dynamics

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions

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Open Problems

But we’re just now starting to understand how timing interacts with network structure & population turnover.

Required: New graph theoretic understanding of dynamic paths

Forward Reachable Sets; Authors: Benjamin Armbruster, Li Wang, Martina Morris

https://arxiv.org/abs/1605.03241

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

At the macro level: models that allow for real-time feedback & data updates, population dynamics, etc. It's doable now in a compartmental framework but largely ad hoc

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

Current approaches cannot solve the numbers of clusters problem unambiguously. This signals a miss-specified question.

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions

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Open Problems

Need methods that can make sense of evolving group structures. “Identity Arc” model is the right direction.

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

…likely a theory problem. “group” is the intersection of cohesion and exclusion but we don’t distinguish those with our methods.

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions

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Open Problems

003

(0)

012

(1)

102

021D

021U

021C

(2)

111D

111U

030T

030C

(3)

201

120D

120U

120C

(4)

210

(5)

300

(6)

Intransitive

Transitive

Mixed

Triads capture the essence of sociality: only with 3 do you get supra-individual characteristics:

A friend of a friend is a friend…

My partner’s partner is my rival…

A periodic table of social elements

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

The macro structure of a network is thus summarized by the distribution of triads.

Type Number of triads

---------------------------------------

1 - 003 21

---------------------------------------

2 - 012 26

3 - 102 11

4 - 021D 1

5 - 021U 5

6 - 021C 3

7 - 111D 2

8 - 111U 5

9 - 030T 3

10 - 030C 1

11 - 201 1

12 - 120D 1

13 - 120U 1

14 - 120C 1

15 - 210 1

16 - 300 1

---------------------------------------

Sum (2 - 16): 63

Combining elements gives you molecules…

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

We need to extend this work to continuous distributions of triads.

We’re close: ERGM-style simulations build random draws from the subset of possible graphs…but we have no analytic solution.

Triad constraints 🡪 macro-structural constraints

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

Parent

Parent

Child

Child

Child

Positional models are fundamentally under-developed; yet hold the greatest promise of realizing the potential of relational models to provide deep insights into social organization and behavior.

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

Example: Social Exchange in developing contexts

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

Example: Social Exchange in developing contexts

Required: probably need to include content of relation in the theory (at least valence, likely more)

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

Do we know how relations should change over time?

  • A 4 year old should not relate the same way to parents as a 14 year old.
  • But what about old friends?
  • Neighbors? Etc.?

What is the life-history of a relation?

We have no data on the long-term dynamics of relations, outside of some bits on spouse/partner.

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

The real controversy over the Framingham studies turned on social mechanism: how do relations get “inside”?

Current models are largely passive transmission or stress-response; both seem much too simple.

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

Networks exist within an institutional context; only way to know that is to return to communities

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

Deep: Radio collar studies of people might be a bit much, but we leave clear digital traces…can we use that smartly? Safe-graph data & Covid is a good case study.

Probability:

Network Scale Up?

Aggregated Relational Data (ARD)?

Network Sampling With Memory (i.e. smart RDS?)

When do these work? For what sorts of relations? Or network Processes?

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

Ego-centric designs are the most tractable way to collect network data.

To get sociometric insights from local networks, extend k-steps.

A “network hyper-sample” is one possible solution?

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling
    • Missing Data

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

Peer

Behavior

Substantively, peers and behavior co-constitute each other in a naturally endogenous and over-determined way. Notions of partialing out the causal effect of peers on behavior net of behavior on peers miss-asks the question.

We need some radical new thinking on this.

Is not equal to

Peer

Behavior

+

Peer

Behavior

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

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Open Problems

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

Y

X1

X2

Want this

Weak instruments bias us toward null effects

Y

X1

X2

I

Get this

Ignore this

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Open Problems

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

Statistical turn in networks in the 1990s🡪 has dramatically changed the landscape.

But focus on statistical modeling has turned network analysis into “just another” GLM.

That’s a thin portrait of what a network is and should be.

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Article Length (estimated words)

Goodman (1974)

Padgett & McLean (2006)

Maris (1970)

Aral & Van Alstyne (2010)

Goldstone (1986)

Powell et al. (2005)

Boorman & White (1976)

DiMaggio et al. (1996)

Giordanno et al. (2002)

Estimated number of words per paper, ASR/AJS

Open Problems

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Open Problems

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

Statistical turn in networks in the 1990s🡪 has dramatically changed the landscape.

Focus should be on what we can learn.

  • Too often the statistical model replaces theory (i.e. is the term available in the package?)

  • Knee jerk calls to use tools that are not necessary
    • Every dynamic network problem is not an SAOM.

  • Network models don’t fit that well.
    • Dig deep into the predicted network that a model assumes, almost always misses the interesting parts.

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Open Problems

  1. Measures/Metrics:
    1. Dynamic Diffusion
    2. Community Detection
    3. Topological inference

  • Theory:
    • Roles & Multiplex Network dynamics
    • Network “life history”: relational evolution
    • Health Mechanisms

  • Data:
    • Return to community studies
    • Network Sampling

  • Models/Scientific Approach:
    • Proper place for causal models
    • Stop turning networks into regressions
    • How will AI /graph embeddings change our work?

The dramatic rise of AI promises to disrupt how network analysis is done.

What do we want it to do?

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THANK YOU!!