The document explores the spread of rumors on social media through a mathematical lens using graph theory. It discusses various graph-based models, such as the SIR model and the threshold model, to analyze rumor dynamics, as well as strategies for countering their spread. The conclusion highlights the rapid transmission of rumors influenced by individual beliefs and sharing behaviors.

1. A Mathematical Approach to the
Spread of Rumors on Social Media:
Using Graph Algorithm Theory
• Sanjida Alam (232-15-898)
• Sadia Islam Shanta ( 232-15-082 )
• Afia Anzum (232-15-385)
• Lamia Tabassum (232-15-929)
• Suraiya Anam Mouri (232-15-877)
Presente
d by
group 3

2. Table of content
Introduction
Objectives
Theoretical Background
Graph-Based Rumor Models
Applications of Graph Theory
Strategies to Counter Rumor Spread
Challenges and Limitations
Conclusion

3. Introduction
Rumors and their impact
on society
Understanding their
dynamics on social
networks
Overview of
mathematical modeling
in social phenomena

4. Objectives
The dynamics of
rumors
propagation.
Mathematical
models
Strategies
to Counter
Rumor
Spread

5. Theoretical Background
Network Topology Scale-Free
Networks: Social
media graphs often
follow this structure,
where a few nodes
(influencers) have a
high degree, while
most have a low
degree.
Small-World
Networks: Social
networks exhibit
short average path
lengths and high
clustering, aiding
rapid rumor spread.
Centrality
Measures
Degree Centrality:
Identifies nodes with
the most direct
connections
Betweenness
Centrality: Measures
a node's importance
in connecting
different parts of the
network.
Closeness
Centrality:
Indicates how
quickly a node
can spread
information.
Graph
Representation
Nodes
(Vertices):Repres
ent individual
users in a social
network.
Edges:
Represent
relationships or
interactions,
such as
"following" or
"messaging.
"Weight of
Edges: Reflects
the strength of
interaction .
Directed Graphs:
Used when
relationships are
not reciprocal

6. Graph-Based Rumor Models
SIR Model (Adapted for
Rumors)Nodes states:-
Susceptible (S): Unaware of the
rumor Infected (I): Spreading
the rumor Recovered (R):
Stopped spreading the rumor
Edges determine the probability
of state transition between
connected nodes.
Threshold Model :Each
node has a threshold for
adopting a rumor,
influenced by the fraction
of its neighbors spreading
the rumor.
Independent Cascade
Model: Nodes have a
fixed probability of
influencing their
neighbors to adopt the
rumor upon activation.

7. Applications of Graph Theory
Identifying
Super
Spreaders
Nodes with
high degree
or centrality
can be
targeted for
intervention
to curb the
spread.
Rumor
Containme
nt
Strategies
Breaking
critical
edges
(connections
) to reduce
network
connectivity.
Introducing
counter-
information
nodes to
spread
factual
information.
Simulation
and
Prediction
Graph-based
simulations
help predict
the spread
and evaluate
the
effectiveness
of mitigation
measures.

8. Strategies to Counter Rumor Spread
Identify Influential
Nodes
Containment of
Rumor Spread
Monitoring and Early
Detection
Optimized Counter-
Rumor Spread
Visualization and
Analysis

9. Challenges
and
Limitations
• Data-Related Challenges
• Algorithmic Limitations
• Evaluation and Feedback
• Behavioral and
Psychological Challenges
Using only graph algorithms to counter the
spread of rumors comes with several challenges
and limitations.

10. Conclusion
In this presentation, we studied how rumors
spread on social media using mathematical
models.We used equations to describe how information
flows between people and how it can influence others.The
results showed that rumors can spread quickly, but the
spread depends on factors like the number of people
involved, how strongly they believe the rumor, and how
they share information.

11. Thank you​
!