Can network science be taught with a gamified approach? These are the slides i use for an introductory lesson about network science basics. The teaching methodology is inductive. First part (pp 1-42) The five main topics (nodes and links, centrality, in-degree and out-degree, diffusion through networks, degrees of separation) are presented through a concrete case. Students have a game to answer, in presence and/or on line, for each subject. This interactive phase activate their interest and curiosity. Second part (pp 43-58) Each game is recovered, and the experience of the game is explained and connected with the relative concept of network science. Third part (59-68) At the end there is a meta-reflection the gamified experience, talking about the “what” (contents about network complexity) and the “how” (modalities to sustain engagement).

1. Complexity
Play&Learn
Massimo Conte
November 15th, 2021
«Design Issues» Course, prof. Antonella Sbrilli
Master of Science in Product and Service Design

2. BIO
E-learning Manager, Instructional Designer
 E-learning manager and Instructional Designer with 15 years
of experience in creation of e-learning courses (tutorials,
serious games, simulations) for large companies
 Lectures for: University of Udine, University of Perugia,
University of L'Aquila, Lumsa University, Il Sole 24 ORE
Business School, Festival of Complexity, Pordenone Design
Week

3. BIO
Editorial Coordinator of Complexity Education Project
www.complexityeducation.com

4. AGENDA
A) Five games about networks
B) Theory behind the games:
how do the networks work?
C) Meta-evaluation: What and
How of a gamified lesson

5. MEMORABLE MOMENTS
Think about the most memorable
lesson you ever had…
Credits picture: from movie “Dead Poets Society"
Think about the most memorable
game you ever played…
Why do you remember them?

6. WHAT IS COMPLEXITY?
How the knowledge of networks can help us to face the
complexity of systems, phenomena, organizations and social
problems?
Let's see together the video «The power of networks» by RSA
Animate
https://www.youtube.com/watch?v=nJmGrNdJ5Gw

7. KEY POINTS
In the second half of 20th century we started the reasoning about
problems of “organized complexity”, like systems

8. KEY POINTS
Understanding ecosystems is a complex matter,
because there isn’t a linear direct cause-effect relationship

9. KEY POINTS
The tree metaphore
representation of Knowledge
is no longer sufficient
Wikipedia: network structure,
with a strongly
"interconnected" knowledge

10. KEY POINTS
Map of collaborations among
programmers in Perl code
The social structure of network
includes our social relationships
(online and offline)

11. LET’S PLAY WITH NETWORKS
We’ll explore the main concepts about network characteristics.
Everytime you’ll see a box like this…
…it’s your turn to play with Questions and Answers about network
complexity
Credits picture: Robert Collins on Unsplash
Reference for the games:
HARRINGTON, H.,
BEGUERISSE-DÍAZ, M.,
ROMBACH, M., KEATING, L.,
& PORTER, M. (2013).
Commentary: Teach network
science to teenagers.
Network Science, 1(2), 226-
247.

12. 1) NODES AND LINKS
The study of networks is part of discrete mathematics and is based
on graph theory, whose birth dates back to the solution proposed in
1736 by Euler to the "problem of the Königsberg bridges"
Is it possible to complete the route by visiting all the
zones, crossing each bridge only once?
Pregel
river

13. 1) NODES AND LINKS
Is it possible to complete the route by visiting all the
zones, crossing each bridge only once?
Zone A
Zone C
Zone B
Zone D

14. Source: http://demonstrations.wolfram.com/TheSevenBridgesOfKoenigsberg/
1) NODES AND LINKS
An invalid solution

15. 1) NODES AND LINKS
Euler's response: IT’S NOT POSSIBLE
 If we replace each neighborhood with a point, and each bridge
with a line connecting two areas:
Nodes A, B, D have three bridges
Node C has five bridges
Degrees of the nodes:
 A → 3
 B → 3
 C → 5
 D → 3
A graph is viable if and only if…
• …has all the nodes (the zones of the city reachable by the
bridges) of even degree (number of connections, i.e.
bridges),
• …or two nodes have odd degree

16. 2) NODES CENTRALITY IN A NETWORK
Mid 1990s: a Stanford PhD Student studied the
World Wide Web as a Large Interconnected Graph
Indexing via Web Crawlers

17. 2) NODES CENTRALITY IN A NETWORK
Which is the most important node of this network?

18. A node is central if the nodes that choose it are important
We see in this graph:
 who chooses (where the
arrow starts from)
 who is chosen (where the
arrow go)
We see in this matrix:
 in line from where the link
starts
 in the column where the link
arrives
It shows made choices and
received choices
2) NODES CENTRALITY IN A NETWORK
Picture Credits: wikipedia

19. Name of Google’s algorithm:
Pagerank (with a reference to
Larry Page, one of the two
founders)
It indexes websites using the
popularity rating of a web page
to define its position in search
results
 «Votes» don’t weigh all the same: the most popular web pages
express, with their links, the most important votes
2) NODES CENTRALITY IN A NETWORK
Picture Credits: wikipedia

20. 3) IN-DEGREE AND OUT-DEGREE
 “Food web” of Arctic sea: ecosystems of prey and predators
 Nodes are the species, the arrows go from preys to predators
If you were called by the government to study the fauna and
propose solutions to save the planet...
What deductions would you make from this network?
Is eaten by

21. 3) IN-DEGREE AND OUT-DEGREE

22. 3) IN-DEGREE AND OUT-DEGREE
 Which are the key species, e.g. the critical nodes for
the system survival?
 What does it mean for a species to have many
inbound links? And many outbound links?

23. 3) IN-DEGREE AND OUT-DEGREE
«In-degree» → inbound
connections (its preys)
High in-degree means:
 Many species to predate
 It would suffer less from the
disappearance of a prey-
species
«Out-degree» → outbound
connections (its predators)
High out-degree means:
 Many predators
 It is a prey for many species, its
disappearance would cause
problems for the ecosystem

24. 4) DIFFUSION THROUGH NETWORKS
VAX: interactive game on epidemics diffusion

25. This is you You + a friend
You with your
closest friends
Your friends have other friends you may not know,
but that all together are your network of contacts
4) DIFFUSION THROUGH NETWORKS

26. If someone in your circle gets sick, the
infection will spread across the
network
If no countermeasure is
taken, soon the whole
network may be infected
4) DIFFUSION THROUGH NETWORKS

27. The likelihood that someone will
spread the infection depends on
how many neighbors he/she have
Here the nodes have been scaled
based on the number of links
Greater the circles, greater the
likelihood they have of infecting
at least one neighbor
4) DIFFUSION THROUGH NETWORKS

28. If we vaccinate the central
node in this network...
…the other nodes are safe
from contagion
4) DIFFUSION THROUGH NETWORKS

29. Which node would you vaccinate first to limit an incoming
epidemic, if just have one shot to do?
4) DIFFUSION THROUGH NETWORKS

30. If an outbreak of an epidemic happened now,
it could infect only one of the two groups
4) DIFFUSION THROUGH NETWORKS
Video example

31. https://www.complexity-explorables.org/explorables/i-herd-you/
«I herd you!» (SIS-model)
When a virus spreads, the individual can be protected in two ways:
 Direct vaccination
 Herd immunity → immunized people reduce the likelihood of
transmission of the virus to unvaccinated people
Transmissibility
of virus
Spreading of
vaccine
White:
susceptible
to virus
Red:
infectious
4) DIFFUSION THROUGH NETWORKS

32. 5) DEGREES OF SEPARATION
L Characteristic length: minimum number of steps that must be
taken on average to reach any node of a network starting from any
other node
Psychologist Stanley Milgram
estimated that it takes an
average of 6 degrees of
separation to connect two
strangers together
Residents in Nebraska and Kansas
were asked to deliver a package
to a contact person in Boston,
indicating its name, employment
and area where he lived, but not
the exact address

33. 5) DEGREES OF SEPARATION
Each participant could
send the package to a
person they knew, who in
their opinion was the
most likely to know the
final recipient
Average number of
intermediaries: 5.2
Picture credits: wikipedia

34. → 128,000 movies, 358,000 actors
and actresses
Bacon Number: if you were in a movie with Kevin Bacon, you have
Bacon Number = 1
https://oracleofbacon.org/
Kevin Bacon is a Hollywood star. His movies: JFK,
Code of Honor, Sleepers, Apollo 13, Sex Crimes,
Mystic River, X-Men
5) DEGREES OF SEPARATION

35. Which of these actors do has the highest Bacon number?
Think about how many "jumps" you need from Kevin Bacon
to get each one…
5) DEGREES OF SEPARATION

36. 5) DEGREES OF SEPARATION

37. 5) DEGREES OF SEPARATION

38. 5) DEGREES OF SEPARATION

39. 5) DEGREES OF SEPARATION

40. 5) DEGREES OF SEPARATION

41. 5) DEGREES OF SEPARATION

42. LET’S DO A PIT-STOP
You may ask: why are we gaming with all these cases?
Picture credits

43. AGENDA
A) Five games about networks
B) Theory behind the games:
how do the networks work?
C) Meta-evaluation: What and
How of a gamified lesson

44. HOW DO NETWORKS WORK?
Observation → Patterns → Theories
Network science is a new discipline, born in the last 20 years
We could say began with Eulero and the problem of the Königsberg
bridges
1) NODES AND LINKS
FOCUS: FROM OBJECTS TO RELATIONS

45. The «scale invariance» networks follow the power law
HOW DO NETWORKS WORK?
2) NODES CENTRALITY IN A NETWORK
FEW nodes with
MANY links
MANY nodes with
FEW links
 Scale free distribution: many
nodes with few links, few
nodes with many links (HUB);
the anomaly is normal
Examples: airlines, the Internet
 Gaussian distribution: nodes
have an average number of
links; without excessive
anomalies
Examples: road networks,
height of people
Number
of
nodes
Number of links
Number
of
nodes
Number of links
Subjects are all
around an
average
number of
values

46. HOW DO NETWORKS WORK?
HUB
Picture credits: A.L. Barabasi, "Linked: The New Science of Networks"

47. HOW DO NETWORKS WORK?
World Wide Web: hyperlinks network on Wikipedia
Credits: Wikipedia, Chris 73
HUB
Paretian distribution: 80% of nodes link to 20% of web pages

48. HOW DO NETWORKS WORK?
«Getting to philosophy»: clicking on the first link in the main text of an
English Wikipedia article, and then repeating the process, usually leads to
the Philosophy article (true for 97% of all articles in Wikipedia)
Explanation: tendency for Wikipedia pages to move up a "classification
chain"
https://www.xefer.com/wikipedia

49. HOW DO NETWORKS WORK?
3) IN-DEGREE AND OUT-DEGREE
Resilience: ability of a system to continues to carry out its mission
in the face of adversity, after being subjected to a disturbance /
damage that changed that state

50. HOW DO NETWORKS WORK?
3) IN-DEGREE AND OUT-DEGREE
Networks are "resilient" ecosystems. If you delete a node, even if
important, the whole system (probably) won’t collapse
Map of Arpanet, 1980

51. HOW DO NETWORKS WORK?
Networks can spread diseases, but also information
We can have both infectious and informative epidemic
4) DIFFUSION THROUGH NETWORKS

52. HOW DO NETWORKS WORK?
NETINF infers a who-copies-from-whom or who-repeats-after-
whom network of news media sites and blogs
http://snap.stanford.edu/netinf/

53. HOW DO NETWORKS WORK?
Meme: ideas, behaviors, pictures that spreads by means of imitation
from person to person, “jumping” from brain to brain
Facebook outage,
October 4, 2021

54. HOW DO NETWORKS WORK?
L. Adamic (2016) “Information Evolution in Social Networks”:
measurement of imperfect information copying mechanism by examining
the dissemination and evolution of thousands of memes, collectively
replicated hundreds of millions of times in the online social network
Facebook
Meme→ from greek «mímēma» that is «imitation»
Posts by users (jokes, warnings, calls to action)
with hundreds of millions of shares
Information evolves over time, according to
fixed patterns, as if it were a biological
organism
Some memes have a better chance of
“reproducing” than others, based on the ability
of the initial meme to adapt to the different
user niches
Source: http://www.ladamic.com/papers/infoevolution/MemeEvolutionFacebook.pdf

55. We also talked about «small-world»
networks: two people in the network can
reach each other through a short sequence
of acquaintances
HOW DO NETWORKS WORK?
5) DEGREES OF SEPARATION
Our globalized world and the web have a similar structure: for example,
in a maximum of 6 steps each of us could reach the president of the
United States or an Australian aboriginal
Small-world networks tend to contain cliques: sub-networks which have
connections between almost any two nodes within them

56. On the web, the degrees of separation drop below 4
Facebook social graph 2016: average of 3.57 degrees of separation
HOW DO NETWORKS WORK?
Estimated average degrees of separation between all people on Facebook
Source: Facebook, https://research.fb.com/three-and-a-half-degrees-of-separation/

57. We have few degrees of separation also on Wikipedia
Shortest path: minimum number of edges that must be traversed
to travel from the starting node to the destination node
HOW DO NETWORKS WORK?
https://www.sixdegreesofwikipedia.com/

58. Let’s play with shortest paths!
HOW DO NETWORKS WORK?
https://dlab.epfl.ch/wikispeedia/play/

59. AGENDA
A) Five games about networks
B) Theory behind the games:
how do the networks work?
C) Meta-evaluation: What
and How of a gamified lesson

60. HUMAN FOCUSED DESIGN: WHY WE DO THINGS
Octalysis Framework: 8 core drives of gamification, motivating
people towards activites
More info: https://yukaichou.com

61. HUMAN FOCUSED DESIGN: WHY WE DO THINGS
Doing something greater
than yourself → call to
action
Making progress,
developing skills,
overcoming
challenges → Points,
badges
Engagement in a
creative process where
you can try different
combinations → Legos
Feeling of owning
something, like
your avatar →
Collecting stamps
Mentorship,
acceptance,
competition and
envy → Social
networks
Wanting something
because you can’t
have it→ Loyalty
Programs
Finding out what will
happen next →
Gambling addictions
Avoidance of something
negative happening→
discounts expirations
More info: https://yukaichou.com

62. HUMAN FOCUSED DESIGN: WHY WE DO THINGS
Save the planet!
Find a solution to
Königsberg bridges
Seeing what
voted other
students
Countdown for
each game
Curiosity about
next game
Guess degrees of
separation

63. INTERACTIVE CONTENTS
Networks: complex systems, with emergent
behaviors and dynamical process
https://www.complexity-explorables.org/
Each explorable contains one interactive component and describes a single
system. The models are chosen in such a way that the key elements of a
system’s behavior can be explored and explained without too much math
and with as few words as possible

64. INTERACTIVE CONTENTS
Contents: paradigm of
complexity, with a focus on
network science
Modalities: interactions to
sustain engagement

65. META-EVALUATION
Let’s think about this lesson:
 WHAT: we live in
complex networks
 HOW: inductive reasoning and
interactive games to sustain
curiosity and motivation
Playful experiences connect emotions and learning
In a game we accept rules and limits and
we use our creativity

66. CONCLUSIONS: WE LIVE IN A CONNECTED WORLD
Connected: The Power of Six Degrees
Documentary about the origin of network science

67. Complexity Play&Learn
Massimo Conte
November 15th 2021
«Design Issues» Course, prof. Antonella Sbrilli
Master of Science in Product and Service Design
Let’s get in touch for any question:
conte@complexityeducation.com
www.complexityeducation.com
www.linkedin.com/in/conte/

68. REFERENCES
 Barabasi A.L., Network Science, Cambridge University Press, 2016
http://barabasi.com/networksciencebook/
 Eletti V., slideshare https://www.slideshare.net/valerioeletti
 Harrington H., Beguerisse-díaz M., Rombach M., Keating L., & Porter
M. (2013). Commentary: Teach network science to teenagers.
Network Science, 1(2), 226-247. doi:10.1017/nws.2013.11
 Lee SH, Kim P-J, Ahn Y-Y, Jeong H (2010) Googling Social
Interactions: Web Search Engine Based Social Network Construction.
PLoS ONE 5(7): e11233