This document summarizes a presentation given at the International Workshop on Complex Systems Dynamics in August 2021. The presentation discusses modeling sustainability in social networks using a "being hermeneutics" approach. This approach models reality as complex systems of beings characterized by sustainable states of being and information content. Network models discussed include Erdos-Renyi random graphs, Watts-Strogatz small world networks, Barabasi-Albert scale-free networks, and a topology breeding approach. The presentation also discusses modeling the "sense of self" that drives agent behaviors, including aspects like rational empathy, risk aversion, elastic identity, and regional vs. global identities.

1. International Workshop on Complex Systems Dynamics, IIT Madras, August 2021.
Modeling Sustainability
in Social Networks
Srinath Srinivasa
Web Science Lab
IIIT Bangalore
sri@iiitb.ac.in

2. Web Science
Lab
Established in 2002 as Open Systems
Lab focusing on modeling and
analytics of Complex Network
Structured Data
Changed to Web Science Lab in 2015.
Current strength: 6 PhD students, 1
postdoc, 3 MS Scholars, 22
MTech/iMTech project associates
Research verticals: Digital
Capabilities, Data Driven Governance,
Social Cognition, Responsible AI
2

3. Artificial vs Natural Engineering
Made of parts custom built for a specific purpose
Well-defined functionality for each part
Structure designed apriori into its present shape
Imperative design
Made of generic agents capable of playing
several roles
Autonomous actions by agents based on self-
interest and utility maximization
Structure a result of evolution and local
adjustments
Declarative design,
Sense of Self
3

4. Machine vs “Being” Hermeneutics
Machine hermeneutics:
Models reality in terms of inanimate matter, and
interactions between them
Roots from Ancient Greece, greatly popularized
by Newtonian models of physics
Particle foundations for physical reality
Great convergence: mass (matter) = energy
Open question: Energy and Information
Being Hermeneutics:
Models reality as a “holistic” (system of) being,
characterised by sustainable state of being,
information content in different states of being,
etc.
Characteristic of Eastern “dharmic” civilizational
thought
Being: The unit of existence, modeled as a
complex entity comprising of energy and
information
“Consciousness” foundations for reality
4

5. Postulates of “Being”
Primary characteristic is to “be” (settle down in
stable states or configurations)
Under certain closed or boundedness conditions,
collection of beings forms a (system of) being with
its own stable states
Sense of self (Sentient beings)
Individual and collective sense of self
Primary objective: Sustainability of the sense of self
“Being” Oriented System Design
5
Image source: Google image search

6. “Being” Oriented System Design
Postulate of sustainability:
Any closed system of being settles down in a
“low energy” stable state. Visible in physical
systems as elasticity, inertia, ionic interactions,
etc. and in biological systems as homeostasis.
Sentience: Systems of being with a “sense of
self”. Stable states are based on sustenance of
the sense of self, rather than on just physical
low-energy configurations.
Being: A specific form of agency. We will be
using the term “being” and “agent”
interchangeably in this work.
Being and its Environment:
Consider agent a, having its sustainable state
(w.l.o.g represented as a single state), as d(a)
Any agent interacting with a bounded environment
(called vidhi, represented as v(a)) over finitely many
interaction choices, is guaranteed to have a state
of equilibrium representing the “mutual best-
response” function. (Nash’s Theorem:
https://mathworld.wolfram.com/NashsTheorem.htm
l)
Let this equilibrium state be represented as
e(a,v(a)).
6

7. “Being” Oriented System Design
“Manageable” Complex Systems:
7
Tractabl
e
Mangeable Intractable
Machines
Linear
Tractable / Predictable
Dynamics by design
Beings
Non-Linear
Ergodic / Bounded state
space with invariants
Intractable, but manageable
due to invariant stable
properties
Chaos
Non-Linear
Non-Ergodic
Intractable, may have no
invariant / stable states

8. Networks of Beings
Understanding emergence of classes
of network topologies from individual
decision-making
Or
Understanding underlying priorities
of a population by their resultant
network structure
8

9. Erdös-Renyi Networks
Simplest formulation of social networks
Assumes social network connections are
formed in random
Consider a set of n nodes. There can be a total
of n(n-1)/2 undirected edges among them.
Model 1: G(n,p):
− Choose a set of m=p*n edges from this set in
random and add them to the graph
Model 2: H(n,p):
− Each of the n(n-1)/2 edges is added to the
graph with a probability p
By Vonfrisch, CC BY-SA 3.0,
https://commons.wikimedia.org/w/index.php?curid=3469734
9

10. Erdös-Renyi Networks
Largest Connected Component (LCC):
Most powerful community in the network
With uniform probability of addition of edges,
size of LCC undergoes an inflection when the
number of edges is approximately n/2, growing
rapidly till it start saturating approximately
around 2n edges.
Diameter of LCC increases with inflection, and
starts reducing when the LCC size saturates.
“With greater connectivity, world (LCC) grows
bigger before it grows smaller.”
10

11. Triadic Closure
Informally: Two people who have a common
friend are likely to become friends themselves.
The more closer they are to their common
friend, the more likely is it that they become
friends themselves
Triadic closure is not a property of how people
behave-- it is a network property
If “A is acquainted with B” implies “A spends
time with B” then increasing amount of
acquaintance between A, B and A,C within a
given time period results in B and C spending
time with each other (pigeon-hole principle)
Entrenchment: Triadic closure property creates an
effect of “entrenchment” in acquaintance networks
(Image Source: [Easley and Kleinberg 2010])
Entrenched networks low in novelty, high in mutual
familiarity (and hence, trust), thus lowering
bookkeeping costs (at the expense of novelty)
11

12. Watts-Strogatz Model
Refinement over the Erdos-Renyi random graph model
to accommodate triadic closure
1) Consider N nodes to be on a ring lattice labeled [0,
N-1]
2) Construct a (deterministic) graph having Nk/2 edges
by connecting each node to k/2 neighbours each on
its right and left.
3) For every node, choose one of the edges created in
step 2, and break it with a probability ß (0 ≤ ß ≤ 1)
4) Rewire the broken edges and connect them
randomly to any node in the graph
12

13. Watts-Strogatz Model
When ß = 0, the graph is a deterministic graph
with maximum possible triadic closure with k
edges
Creates a “resilient” network structure with a
Hamiltonian circuit: diameter no greater than
n/2, connectivity no lesser than 2, deterministic
routing with local knowledge.
Characteristic feature of entrenched
communities in human societies: high trust,
high familiarity, high resilience, low novelty.
When ß = 1, the Watts-Strogatz model is
equivalent to an Erdos-Renyi model G(n,p)
where:
When ß = 0, the graph has a deterministic
regular or near-regular structure. With ß = 1, the
degree distribution is known to be Poisson.
Degree distributions in real-world social
networks are known to be have a “hub and
spoke” (power-law, log-normal, etc.) “scale-
free” property, giving it short diameters (also
known as “small world” networks).
13

14. Barabasi-Albert Model
Generates a “hub-and-spoke” topology with a
power-law degree distribution:
“Scale-free” and “small-world” properties
Resilient against random failures, but
susceptible to “targeted attacks” (unlike WS
networks with clustering links)
De I, Keiono, CC BY-SA 2.5,
https://commons.wikimedia.org/w/index.php?curid=2459900
14

15. Barabasi-Albert Model
Preferential Attachment
Generative model for scale-free graphs:
1. Start with a small set of “seed” nodes
connected randomly
2. For every subsequent incoming node:
a. with probability γ connect to any existing
node at random
b. with probability 1-γ, connect to node k with
probability π(k), where:
where α > 0
Scale-free networks are known to be ubiquitous
in nature and emergent human networks: Blood
circulatory network, Global aviation network,
Internet topology, etc.
B-A networks are known to be resilient against
“random failures” -- i.e. failure of any k nodes
chosen at random will w.h.p. not partition the
network.
But they are not resilient against “targeted
attacks”-- failure of a small set of key hubs can
easily partition the network.
R. Cohen, K. Erez, D. Ben-Avraham, S. Havlin (2000). "Resilience of
the Internet to random breakdowns". Phys. Rev. Lett. 85: 4626. 15

16. Topology Breeding
Human social networks exhibit properties of
both entrenchment (WS network) and scale-free
resilience (BA network), showing resilience
against both random failures and targeted
attacks.
“Topology Breeding” an attempt to generate
networks with properties of both BA and WS
networks.
Given a society of n agents (beings):
Each agent has some “sustainability needs” which may
be potentially met by other agent in the network.
Each connection incurs a cost and brings some value
The way connections are made across the network may
give the network some “robustness” or resilience
against failure of agents and edges
Communication network has three optimization criteria:
Efficiency
Robustness
Cost 16
Patil, Sanket, Srinath Srinivasa, Saikat Mukherjee, Aditya Ramana Rachakonda, and
Venkat Venkatasubramanian. "Breeding diameter-optimal topologies for distributed
indexes." Complex Systems 18, no. 2 (2009): 175.
Patil, Sanket, Srinath Srinivasa, and Venkat Venkatasubramanian. "Classes of
optimal network topologies under multiple efficiency and robustness constraints." In
2009 ieee international conference on systems, man and cybernetics, pp. 4940-4945.
IEEE, 2009.

17. Topology Breeding
Use of genetic algorithms to find optimal topologies
under different constraints over efficiency, robustness
and cost
Infrastructure cost is bounded by giving each node
exactly k edges to make connections with other nodes
so as to minimize distance to all nodes, and maximize
connectivity.
Topologies generated from individual runs are
combined using a cross-over function to overcome local
minima. Topologies with lower fit functions are
discarded. Fit calculated by a parameter α that trades between
efficiency and robustness
17

18. Topology Breeding
Star topology
Emergent topology when α = 1 (100% importance to
efficiency and 0% importance to robustness)
Star has the smallest degree of separation for a
network of n nodes and (k=1) edge per node.
Ring topology
Emergent topology when α = 0 (100% importance
to robustness and 0% importance to efficiency)
Circle is has highest resiliency (connectivity = 2)
against targeted attacks under the cost
constraints (k=1) 18

19. Emergent topology when α is set to some value
between 0 and 1 (and cost factor k = 1) were a
family of topologies combining the circle and
star.
Displayed properties of “hub and spoke” with a
small diameter and a scale-free degree
distribution, and connectivity of at least 2 for a
large subset of the graph.
Degree distribution in the hub and spoke
resembles a power-law
Topology Breeding
19

20. Topology Breeding
With α = 1 (maximum emphasis on efficiency or
diameter reduction, and minimum emphasis on
resilience or connectivity), maximum
permissible degree (p) and number of edges (e)
were varied, with n=20 nodes.
Result is a class of tree/star structured
topologies until e=20, and then topologies with
a core ring (connectivity ≥ 2) with spokes
connecting to the core.
Degree distributions approximated by a power
law.
20

21. Topology Breeding
With α = 0 (minimum emphasis on efficiency or
diameter reduction, and maximum emphasis on
resilience or connectivity), maximum
permissible degree (p) and number of edges (e)
were varied, with n=20 nodes.
Result is uniformly a class of circular skip lists
(CSL) (connectivity ≥ 2) with no spokes-- only
chords. Degree distributions still approximated
by a power law (unlike WS networks).
CSL has properties of both WS and BA networks, and can be
resilient to both random failures and targeted attacks while
optimising on efficiency. Seems to appear in real world banking
networks. 21
Lux, Thomas. "Emergence of a core-periphery
structure in a simple dynamic model of the
interbank market." Journal of Economic Dynamics
and Control 52 (2015): A11-A23

22. Sense of Self
Basic unit of sustainability.
Agency is modeled as an optimization process
of utility maximization, driven by “self-interest”
While much research has focused on strategies
for utility maximization, relatively little interest
has gone into (computationally) modeling the
“sense of self” that drives self interest.
Classical model
From the theory of games and rational choice, by
von-Neumann and Morgenstern.
Self-interest (and the idea of “Self” itself) modeled as
a preference relation across pairs of choices: Strong
preference (>), Weak preference (≥), Indifference (||)
Valuation modeling: If A > B > C, and choice I returns
B with probability 1, while choice II returns A with
probability p, and B with probability 1-p.
The choices are said to be indifferent when for some
value of p, E(II) = E(I), or p v(A) + (1-p) u (C) = u(B)
22

23. Sense of Self
Rational Fools:
Critique of classical model by Amartya Sen.
Argues that it is too simplistic to reduce “sense
of self”
Human sense of self contains at least the
following extra elements:
● Rational Empathy
● Sense of fairness
● Basic level of trust
If humans were strict rational maximizers, above
kinds of interactions would be more
commonplace.
23
Agents pursuing “Rational empathy” (Pareto
improvements, rather than rational
maximization), can agree to cooperate in a one-
shot PD game.

24. Sense of Self
Risk Aversion:
Kahnemann and Tversky in their work on
“prospect theory” show that the human sense of
self does not treat the prospect of gains and
losses symmetrically.
Fund I, requires investment of Rs. 5000, and has a
guaranteed return of Rs. 7500 at the end of its
term. Fund II, requires investment of Rs. 5000, and
returns either nothing or Rs. 15,000 with equal
probability.
Both funds have same expected utility in classical
model, but humans shown to prefer Fund I over
Fund II.
Utility of prospects of gains saturate with more
expected gains (diminishing value of returns),
while utility of prospects of losses, grows with a
high negative slope.
24

25. Sense of Self
Elastic sense of identity:
Human sense of self is not a monolithic entity.
Humans often “identify” with external objects and
concepts, by making it a part of their sense of self.
Given agent a, sense of self S(a) given by:
Sa = (I, da, γa), where
I is the “identity set” comprising of objects (including
‘a’ itself) to which, the sense of self is attached, da:
{a} ｘI → R represents “semantic distance” to each
object in I, and 0 ≤ γa ≤ 1 represents the rate at
which identification attenuates.
Agent a identifies with object at distance d with
an attenuation of γa
d
25

26. Sense of Self
Computational Transcendence:
Modeling an elastic sense of identity, where an
agent “identifies” with its neighbour to different
extents.
Modeled as a utility function that combines
payoffs from oneself and neighbour, with
attenuation factor.
When both players “transcend” their sense of
self to include their neighbour to an extent of
(⅓) or more, it makes rational sense to
corporate, rather than defect. 26

27. Sense of Self
Regional and Global Identities:
27
HH HT TH TT
H 6 6 6 6 1 6 1 6 6 10 10 2
T 6 6 1 2 10 10 10 2 10 0 0 0

28. Identity and Sustainability
Regional and Global Identities:
Social identities within communities in a
population often conflict with interests of the
population as a whole, leading to the “salad
bowl” problem of diversity
Ex: Regional vs national language conflicts,
Religion versus nation loyalty conflicts, etc
Homophily: Tendency of an agent to prefer
other agents of the same regional identity,
when establishing new connections
Insularity: Tendency of an agent to distrust by
default, agents belonging to another regional
identity, and trust by default, agents belonging
to the same regional identity.
The extent of homophily and insularity within a
population of regional identities may vary.
28
Jayati Deshmukh, Srinath Srinivasa, Sridhar
Mandyam. What keeps a vibrant population
together? Complex Systems journal. (to appear)

29. Identity and Sustainability
Network evolution:
Agents in a network adopt either one of several
“regional” identities, or a “global” identity
Agents play a game of Iterated Prisoners’
Dilemma (IPD) with their neighbours using the
game matrix shown
Global Agents: Global agents establish new
connections with a probability in proportion to
the degree of the target agent (preferential
attachment)
Network Formation: With a probability hp
(homophily probability), regional agents
connect to other regional agents of the same
identity, and with a probability (1-hp) regional
agents connect rationally, using preferential
attachment.
29

30. Identity and Sustainability
Network Dynamics: With probability ip a
regional agent is flagged as “insular” and “non-
insular” with a probability (1-ip).
Non-insular regional agents, and global agents,
adopt a cooperative TIT-FOR-TAT (TFT)
strategy, that begins with offering cooperation,
and reflecting the previous move from the other
player, in subsequent iterations.
Insular agents adopt a Distrustful TFT (DTFT)
that begins with non-cooperation for agents not
belonging to same identity.
Network Evolution: A given network plays IPD
for an “epoch” τ, after which, links giving a net
negative payoff are discarded and new ones
established according to Network Formation
heuristics.
Network reaches an equilibrium (Pareto
optimality) when all links have positive payoffs.
30

31. Identity and ...
Simulation runs were conducted for four
extreme configurations: Low (20%)/High (80%)
Insularity/Modularity and results calibrated
when network reached equilibrium.
Case 1: No global agents
With no “global” agents, regional agents have
no problem forming a melting pot at LILH, but
break apart into separate clusters at HIHH.
At LIHH or HILH, they form a “salad bowl” of
segregated clusters, but still connected.
31

32. Identity and ...
Case 2: Small number (20%) of global agents
Global agents form the glue that keep the
network connected, in all four cases.
With low insularity, network is less segregated
and has a smaller diameter.
Despite playing a key role in keeping the
network together, global agents neither have
high payoffs, nor high bargaining power based
on Dominance of Neighbours (DON) metric!
32

33. Identity and ...
Average payoffs for global vs regional agents in
all four configurations for Case - 2.
Scatter plot of bargaining power (DON) and payoff
for global and regional agents for Case - 2.
33

34. Identity and ...
Case - 3: High number (80%) of global agents
Global agents overwhelm the network and
create a densely connected melting pot for LILH
and LIHH configurations. When insularity is high
(HILH and HIHH), insular regional agents are
alienated, to the extent that they find it lucrative
to break apart from the network altogether
(HIHH).
34

35. Identity and Sustainability
Average payoffs for global and
regional agents in HIHH
configuration, for variation in the
percentage of global agents.
Global agents’ payoffs lesser than
that of regional agents, till their
population reaches ~75% at which
stage, they alienate insular regional
agents anyway!
Identity needs to be stronger than
rationality to be a global agent!
35

36. Identity and Sustainability
The dynamics of identity:
Our sense of self is elastic, and can be attached
to external concepts and ideas
Identifying with an external entity,
characteristically different from rationally
associating with it
Cooperative behaviour can emerge without
long-term iteration and evolution, with elastic
identity
Regional and global identities:
Global identities are critical to keep a diverse
population of regional identities united
No rational incentive for global identity-- global
agents neither get most wealthy, nor most
powerful
Very large proportion global agents in the
demographics, can alienate regional identities
36

37. Conclusions
“Being-oriented computing” as a potential
modeling paradigm for analyzing and building
manageable complex systems
Elements of being: Resilience (sustainability),
Identity (sense of self)
Current work: Introducing an elastic sense of
self in RL agents for designing responsible AI
Acknowledgments:
Sanket Patil
Aditya Ramana Rachakonda
Prof. Venkatasubramanian (formerly Purdue)
Jayati Deshmukh
Prof. Sridhar Mandyam
37

38. Relevant Publications
Sanket Patil, Srinath Srinivasa, and Venkat
Venkatasubramanian. Classes of Optimal Network
Topologies under Multiple Efficiency and Robustness
Constraints. Proc. of the IEEE Int’l Conference on Systems,
Man and Cybernetics (SMC 2009), San Antonio, Texas, USA,
October 2009, pp. 4940 – 4945
Sanket Patil, Srinath Srinivasa. Theoretical Notes on Regular
Graphs as applied to Optimal Network Design. Proceedings
of the International Conference on Distributed Computing
and Internet Technology (ICDCIT 2010), Bhubaneswar, India,
February 2010.
Patil, Sanket, Srinath Srinivasa, Saikat Mukherjee, Aditya
Ramana Rachakonda, and Venkat Venkatasubramanian.
"Breeding diameter-optimal topologies for distributed
indexes." Complex Systems 18, no. 2 (2009): 175.
Patil, Sanket, Srinath Srinivasa, and Venkat
Venkatasubramanian. "Classes of optimal network
topologies under multiple efficiency and robustness
constraints." In 2009 ieee international conference on
systems, man and cybernetics, pp. 4940-4945. IEEE, 2009.
Jayati Deshmukh, Srinath Srinivasa. Evolution of Cooperation
with Entrenchment Effects. Proceedings of the International
Conference on Autonomous Agents and Multi-Agent
Systems (AAMAS 2015), Istanbul, Turkey, ACM Press, May
2015.
Jayati Deshmukh, Srinath Srinivasa. Cooperation and the
Globalization-Localization Dilemmas. Complex Systems
journal. (to appear)
Jayati Deshmukh, Srinath Srinivasa, Sridhar Mandyam. What
keeps a vibrant population together? Complex Systems
journal. (to appear) 38

39. Thank You!
39