Acquisition of Social Network
Structure
Jason J. Jones
Edge
Link
Connection
Graph Node
Network Vertex
?
Hassan Ghul
Al-Qaeda Courier
(Captured)
“part of this network of haters that we're dismantling ”
Abu Ahmed al-Kuwaiti
Bin Laden Courier
(Deceased)
Abu Musab al-Zarqawi
Leader of Al-Qaeda in Iraq
(Deceased)
Osama Bin Laden
Al-Qaeda Founder
(Deceased)
• How do we learn the structure of graphs?
• How are graph structures represented in
the mind?
• Social networks Graphs
• Graphs are Grammars are Markov Chains
Hypotheses
1. Human subjects will acquire a network’s
structure more quickly if it resembles a true
human social network rather than an arbitrary
network.
2. Human subjects will acquire a network’s
structure more quickly if it is framed as a social
network as opposed to the same network
framed in some other manner (e.g. a computer
or transport network.)
3. Some forms of representation of the network
will lead to faster acquisition than others.
Hypotheses
1. Human subjects will acquire a network’s
structure more quickly if it resembles a true
human social network rather than an arbitrary
network.
2. Human subjects will acquire a network’s
structure more quickly if it is framed as a social
network as opposed to the same network
framed in some other manner (e.g. a computer
or transport network.)
3. Some forms of representation of the network
will lead to faster acquisition than others.
Hypotheses
1. Human subjects will acquire a network’s
structure more quickly if it resembles a true
human social network rather than an arbitrary
network.
2. Human subjects will acquire a network’s
structure more quickly if it is framed as a social
network as opposed to the same network
framed in some other manner (e.g. a computer
or transport network.)
3. Some forms of representation of the network
will lead to faster acquisition than others.
Experiment 1
• 112 subjects
• 2 (Graph, within) x 2 (Training, between)
• 2AFC classification test trials
• Interleaved training and test trials
Manipulation: Graph Type
• Observable human social networks are
scale-free.
– Email Networks
• Ebel, H., Mielsch, L.I., Bornholdt, S. (2002)
– File-Sharing Networks
• Wang, F., Moreno, Y., & Sun, Y. (2006)
– Sex Networks
• Liljeros, F., Edling, C. R., Amaral, L. A. N., Stanley,
H. E., & Åberg, Y. (2001)
Manipulation: Graph Type
• Random Graph • Scale-Free Graph
– Erdős & Rényi (ER) – Barabási–Albert (BA)
Manipulation: Graph Type
For to all those who have, more will be
given, and they will have an abundance;
but from those who have nothing, even
what they have will be taken away.
Matthew 25:29
Manipulation Check
Manipulation: Training
• Edge Training • Network Walk
75
70
Accuracy
Random
65 Graph
60 Scale-Free
Graph
55
50
Edge Walk
Training
75
70
Accuracy
Random
65 Graph
60 Scale-Free
Graph
55
50
Edge Walk
Training
0.5
0.45
Error Rate
Edge
Walk
0.4
Power (Edge)
Power (Walk)
0.35 -0.061
y = 0.3888x
y = 0.4064x-0.0712
0.3
1 2 3 4 5 6 7 8 9 10
Trial (bins of 8)
0.5
0.45
Error Rate
Random
Scale-Free
0.4
Power (Random)
Power (Scale-Free)
0.35 -0.0621
y = 0.4184x
-0.0708
y = 0.3769x
0.3
1 2 3 4 5 6 7 8 9 10
Trial (bins of 8)
Conclusions
1. Subjects acquire
scale-free graph
structure more 75
quickly than random 70
Accuracy
Random
graph structure. 65 Graph
60 Scale-Free
Graph
55
2. The difference 50
between edge Edge Walk
Training
training and walk
training is small or
non-existent.
Hypotheses
1. Human subjects will acquire a network’s
structure more quickly if it resembles a true
human social network rather than an arbitrary
network.
2. Human subjects will acquire a network’s
structure more quickly if it is framed as a social
network as opposed to the same network
framed in some other manner (e.g. a computer
or transport network.)
3. Some forms of representation of the network
will lead to faster acquisition than others.
Experiment 2
• 102 subjects
• 2 (Graph, within) x 3 (Frame, between)
• Frame
– Social Network
– Transport Network
– Computer Network
Manipulation: Graph Type
• Random Graph • Scale-Free Graph
– Erdős & Rényi (ER) – Barabási–Albert (BA)
All Edges Training
Feedback at Test Trial
75
70
Accuracy
Random
65
Graph
60 Scale-Free
Graph
55
50
Social Transport Computer
Surface Description
75
70
Accuracy
Random
65
Graph
60 Scale-Free
Graph
55
50
Social Transport Computer
Surface Description
0.5
Random
0.45 Scale-Free
Power (Random)
Error Rate
Power (Scale-Free)
0.4
-0.0711
y = 0.4625x
0.35 -0.0933
y = 0.4247x
0.3
1 2 3 4 5 6 7 8 9 10
Trial (bins of 8)
0.5
Social
Transport
0.45 Computer
Error Rate
Power (Social)
Power (Transport)
0.4
Power (Computer)
-0.129
y = 0.4404x
0.35
y = 0.4449x-0.1004
-0.0242
y = 0.4469x
0.3
1 2 3 4 5 6 7 8 9 10
Trial (bins of 8)
Conclusions
1. Subjects acquire scale-free
graph structure more quickly
than random graph
structure. (Replicated) 75
70
2. Subjects were slower to
Accuracy
Random
65
acquire the structure of a Graph
Scale-Free
computer network than a 60
Graph
social or transport network. 55
50
Social Transport Computer
3. Performance for computer
Surface Description
networks was so poor, it
diminished the size of the
graph effect.
Experiment 2a
• The same list of names used for social,
transport and network frames.
• 177 subjects
• 2 (Graph, within) x 3 (Frame, between)
• Frame
– Social Network
– Transport Network
– Computer Network
Experiment 2a
Adrasmon Asahan Abiko Alchevsk
Buston Burmeso Bando Bibrka
Chkalovsk Cilacap Chiba Chasiv
Dushanbe Demak Daito Debaltseve
Farkhor Elelim Ena Enerhodar
Ghafurov Fef Fujiidera Fastiv
Hisor Gunung Gamagori Hadiach
Isfara Ilaga Habikino Ichnia
Jomi Jepara Ibaraki Kaharlyk
Khujand Keerom Joso Ladyzhyn
Mastchoh Lotu Kadoma Makiivka
Nurak Mappi Matsubara Nadvirna
Panjakent Nias Nagareyama Obukhiv
Qayroqqum Oksibil Obu Pavlohrad
Rumi Puncak Ryugasaki Radekhiv
Sharora Rantau Saijo Saky
Tursunzoda Sugapa Tahara Talne
Vose Tegal Urayasu Uhniv
Yovon Wonogir Wajima Valky
Zafarobod Yalimo Yachimata Yahotyn
75
70
Accuracy
Random
65
Graph
60 Scale-Free
Graph
55
50
Social Transport Computer
Surface Description
Conclusions
1. The poorer
performance and
interaction in the 75
Computer condition 70
was not replicated.
Accuracy
Random
65
Graph
60 Scale-Free
Graph
55
2. Those effects were 50
probably due to the Social Transport Computer
Surface Description
stimuli sets used in
the previous
experiment.
Hypotheses
1. Human subjects will acquire a network’s
structure more quickly if it resembles a true
human social network rather than an arbitrary
network.
2. Human subjects will acquire a network’s
structure more quickly if it is framed as a social
network as opposed to the same network
framed in some other manner (e.g. a computer
or transport network.)
3. Some forms of representation of the network
will lead to faster acquisition than others.
Training Style
Experiment 1 Experiment 2
(All Edges Train)
Edge Train Walk Train Social Transport Computer
Random Random
Graph Graph
Scale- Scale-
Free Free
Graph Graph
75
70
Accuracy
Random
65
Graph
60 Scale-Free
Graph
55
50
Edge Walk All Edges
Training
75
70
Accuracy
Random
65
Graph
60 Scale-Free
Graph
55
50
Edge Walk All Edges
Training
Conclusions
1. Variations in training
methods seem to
have little effect on 75
graph acquisition. 70
Accuracy
Random
65
Graph
60 Scale-Free
Graph
55
50
Edge Walk All Edges
Training
Stakes Experiment
• 135 subjects
• 3 (Graph, within) x 3 (Stakes, between)
• Stakes
– Class
– Class + You
– Survival + You
Dense
Random
Dense
Scale-Free
Caveman
Class
Class + You
Survival + You
75
70
Accuracy
65 Random
Caveman
60
Scale-Free
55
50
Class Class + Survival +
You You
Stakes
75
70
Accuracy
65 Random
Caveman
60
Scale-Free
55
50
Class Class + Survival +
You You
Stakes
Dense Dense
> Caveman >
Scale-Free p < .001 p = 0.13 Random
Class Survival
Class n.s. n.s.
+ You + You
Conclusions
1. Scale-free graphs
are consistently the
easiest to learn. 75
70
Accuracy
65 Random
Caveman
2. Acquisition does not 60
Scale-Free
55
seem to be 50
obviously affected Class Class +
You
Survival +
You
by framing. Stakes
Egocentric Bias
75
70
Accuracy
65 Not You
60 Is You
55
50
Class Class + Survival +
You You
Stakes
Conclusions
1. Subjects acquire
personally relevant
information more 75
70
readily.
Accuracy
65 Not You
60 Is You
55
2. Graph learning can 50
be directed so that it Class Class +
You
Survival +
You
is node-specific. Stakes
Network Centrality
Centrality
Popularity Position Effect – Scale Free
0.9
Accuracy
0.8
0.7
0.6
0.5
5
5
5
5
5
5
5
5
5
5
0.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Degree of Test Nodes (Mean)
Popularity Position Effect – Scale Free
0.8
Accuracy
0.7
0.6
0.5
0 0.1 0.2 0.3 0.4
Eigenvector Centrality of
Test Nodes (Mean)
Popularity Position Effect – Random
0.9
Accuracy
0.8
0.7
0.6
0.5
5
5
5
5
5
5
5
5
5
5
0.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Degree of Test Nodes (Mean)
Popularity Position Effect – Random
0.8
Accuracy
0.7
0.6
0.5
0 0.1 0.2 0.3 0.4
Eigenvector Centrality of
Test Nodes (Mean)
Conclusions
1. The connection
patterns of low-
centrality and high- 0.8
Accuracy
centrality nodes are 0.7
acquired more 0.6
readily nodes of 0.5
0 0.1 0.2 0.3 0.4
average centrality. Eigenvector Centrality of
Test Nodes (Mean)
What makes a graph easier to
learn?
What makes a graph easier to
learn?
What makes a graph easier to
learn?
Graph Entropy
• Consensus has not
yet formed regarding
how to quantify the
entropy or information
content of a graph.
Graph Entropy
• Network Entropy
Based on Topology
Configuration and Its
Computation to
Random Networks
B.H. Wang, W.X.
Wang and T. Zhou
Graph Entropy
• Information Theory of
Complex Networks:
On Evolution and
Architectural
Constraints
R.V. Sole and S.
Valverde (2004)
Graph Entropy
• Gini Coefficient
• 0 = Perfectly equal
division of edges
• 1 = Top 1 node has
all edges
Prediction
1. Graph structures in which all nodes
have equal degree should be especially
difficult to acquire.
Watts Small World Experiment
• 63 subjects
• 2 (Graph, within) x 2 (Training, within)
• Graph
– Ring Lattice
– Watts-Strogatz Small World
• Training
– Diagram
– Edges
Ring
Lattice
Watts-
Strogatz
Rewiring
Training
Diagram Edge
75
70 Ring Lattice
Accuracy
65
60 Watts-
Strogatz
55 Rewiring
50
Diagram Edge
Training
0.5
Ring
0.45
Watts
0.4 Power (Ring)
Error Rate
Power (Watts)
0.35
y = 0.4059x-0.0922
0.3
y = 0.4059x-0.149
0.25
0.2
1 2 3 4 5 6 7 8
Trial (bins of 8)
0.5
Diagram
0.45
Edge
0.4 Power (Diagram)
Error Rate
Power (Edge)
0.35
y = 0.4361x-0.1167
0.3 y = 0.3752x-0.1226
0.25
0.2
1 2 3 4 5 6 7 8
Trial (bins of 8)
Conclusions
1. The structure of a
regular ring lattice is
easier to acquire 75
than a rewired 70 Ring Lattice
Accuracy
small-world lattice. 65
60 Watts-
Strogatz
55 Rewiring
2. At least in this 50
instance, a diagram Diagram Edge
Training
promotes faster
acquisition.
Hypotheses
1. Human subjects will acquire a network’s
structure more quickly if it resembles a true
human social network rather than an arbitrary
network.
2. Human subjects will acquire a network’s
structure more quickly if it is framed as a social
network as opposed to the same network
framed in some other manner (e.g. a computer
or transport network.)
3. Some forms of representation of the network
will lead to faster acquisition than others.
Hypotheses
1. Human subjects will acquire a network’s
structure more quickly if it resembles a true
human social network rather than an arbitrary
network.
2. Human subjects will acquire a network’s
structure more quickly if it is framed as a social
network as opposed to the same network
framed in some other manner (e.g. a computer
or transport network.)
3. Some forms of representation of the network
will lead to faster acquisition than others.
Hypotheses
1. Human subjects will acquire a network’s
structure more quickly if it resembles a true
human social network rather than an arbitrary
network.
2. Human subjects will acquire a network’s
structure more quickly if it is framed as a social
network as opposed to the same network
framed in some other manner (e.g. a computer
or transport network.)
3. Some forms of representation of the network
will lead to faster acquisition than others.
New Experiments Running
1. Training out yes bias
2. Facebook predictors of learning rate
3. Simultaneous networks
70
65
Accuracy
V1 Female
60
V1 Male
55
50
V2 Female V2 Male
70
65
Yes Bias
V1 Female
60
V1 Male
55
50
V2 Female V2 Male