Enhancing Graph Clustering in Dynamic Networks with Distributed
Online Life-Long Learning
Hariprasauth Ramamoorthy
a
, Rajkumar Vaidyanathan
b
and Suresh Sundaram
c
Indian Institute of Science, Bengaluru, Karnataka, India
Keywords:
Graph-Based Clustering, Distributed Online Life-Long Learning (DOL3), Social Network Analysis, Trust
and Reputation, Multi-Agent System, Trust, Dynamic Network.
Abstract:
Trust and reputation assessment are critical in dynamic environments like recommendation systems, biolog-
ical network and social networks. Malicious agents tend to collude to manipulate the reputation for selfish
reasons. However, traditional methods struggle to adapt to the evolving relationships and interactions within
these networks. This paper introduces a novel approach that integrates Distributed Online Life-Long Learning
(DOL3) with graph clustering to address the challenge of collusion. By enabling agents to continuously learn
and update their clustering models, our approach enhances the system’s ability to detect malicious agents,
maintain trust, and ensure the integrity of reputation scores. We present a detailed mathematical formulation
of our algorithm, incorporating local clustering models, distributed consensus, and model adaptation. Experi-
mental results on the Cora dataset demonstrate the superior performance of our approach compared to existing
methods, particularly in terms of accuracy (by 11.8%) and adaptability to dynamic and complex network sce-
narios. The accuracy is measured using Normalized Mutual Information (NMI), a robust metric for comparing
predicted and actual cluster assignments. Our findings highlight the effectiveness of DOL3-enhanced graph
clustering in addressing the challenges of trust and reputation assessment in dynamic environments.
1 INTRODUCTION
Graph clustering is a fundamental task in network
analysis, with applications in various domains such
as social networks, biological networks, and recom-
mendation systems. The goal of graph clustering is to
partition a graph into groups of nodes (clusters) that
are densely connected within themselves but sparsely
connected to other clusters. Traditional graph cluster-
ing algorithms often assume static networks in which
the relationships between nodes remain constant over
time. However, in many real-world scenarios, net-
works are dynamic and evolve due to changes in node
attributes, edge weights, or the addition/removal of
nodes. These dynamic changes can significantly im-
pact the accuracy and relevance of the clustering re-
sults (Sievers, 2020).
To address the limitations of traditional graph
clustering algorithms, this paper proposes a novel ap-
proach that integrates Distributed Online Life-Long
a
https://orcid.org/0009-0004-4922-0319
b
https://orcid.org/0009-0002-2577-0813
c
https://orcid.org/0000-0001-6275-0921
Learning (DOL3) with graph clustering. DOL3 en-
ables agents to continuously learn and adapt their
models in a distributed manner, making them well
suited for dynamic environments. The contributions
of this paper are as follows:
• DOL3-Based Graph Clustering Framework: We
introduce a framework that integrates the novel
DOL3 with graph clustering, allowing agents to
adapt their clustering models to changing network
dynamics.
• Mathematical Formulation: We provide a detailed
mathematical formulation of the proposed algo-
rithm, including the local clustering models, dis-
tributed consensus mechanism, and the model
adaptation process.
• Experimental Evaluation: We conducted experi-
ments on synthetic and real-world datasets to eval-
uate the performance of our approach and com-
pare it with existing methods.
In the context of multi-agent systems, trust refers
to the belief that an agent will act in a way that is ben-
eficial to another agent, even in the absence of direct
monitoring or enforcement. Reputation is a collective
80
Ramamoorthy, H., Vaidyanathan, R. and Sundaram, S.
Enhancing Graph Clustering in Dynamic Networks with Distributed Online Life-Long Learning.
DOI: 10.5220/0013167100003890
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 17th International Conference on Agents and Artificial Intelligence (ICAART 2025) - Volume 1, pages 80-90
ISBN: 978-989-758-737-5; ISSN: 2184-433X
Proceedings Copyright © 2025 by SCITEPRESS – Science and Technology Publications, Lda.

assessment of an agent’s trustworthiness based on the
opinions and experiences of other agents. Some of
the examples of dynamic network include social net-
works, biological networks, e-commerce recommen-
dation systems, etc. (Govindaraj et al., 2021). It is
often used as a proxy for trust, as it reflects the con-
sensus view of an agent’s behavior. Similar online
learning approaches have also been used in the area
of robotics (Gupta and Sundaram, 2023). This paper
proposes a novel approach that integrates Distributed
Online Life-Long Learning (DOL3) with graph clus-
tering to address the challenges of trust and reputation
assessment in dynamic networks. DOL3 empowers
agents to continuously learn and update their cluster-
ing models, enhancing the system’s adaptability and
robustness. By combining DOL3 with graph cluster-
ing, we aim to improve the accuracy and efficiency of
identifying malicious agents and maintaining the in-
tegrity of reputation scores. Our proposed algorithm
offers several key advantages:
• Adaptability: DOL3 enables agents to continu-
ously learn and adapt their clustering models to
changing network dynamics, making the system
more resilient to evolving conditions.
• Accuracy: By combining graph clustering with
DOL3, we achieve improved accuracy in identi-
fying malicious agents and assessing trustworthi-
ness.
• Efficiency: Our approach is computationally ef-
ficient, making it suitable for real-world applica-
tions with large-scale networks.
The remainder of this paper is organized as fol-
lows: Section 2 provides a background on trust and
reputation systems, graph clustering, and DOL3. Sec-
tion 3 presents the proposed DOL3-enhanced graph
clustering algorithm. Section 4 describes the experi-
mental setup and evaluation methodology. Section 5
presents the experimental results, comparing our ap-
proach to existing methods. Finally, Section 6 con-
cludes the paper with a summary of our findings and
potential future directions.
2 RELATED WORK
There are models and studies in the area of Graph
Clustering, Colluding Agents and the assessment of
Trust and Reputation. This section explains the key
related works in these areas and their underlying prin-
ciples that drove the motivation behind this paper.
Graph clustering, a fundamental task in data mining
and machine learning, involves partitioning a graph
into subsets of nodes, such that nodes within the same
subset are more similar to each other than those in dif-
ferent subsets. This section also outlines the integra-
tion of graph clustering with the trust assessment.
2.1 Graph Clustering and Learning
Graph clustering, also known as community detec-
tion, aims to identify groups of nodes (agents) that
are densely connected within themselves but sparsely
connected to other groups. Various algorithms have
been proposed for graph clustering, including:
• Modularity-based methods: These methods op-
timize a modularity score to identify commu-
nities (Ghosh et al., 2019). Examples include
Louvain Modularity Optimization (Seifikar et al.,
2020) and Girvan-Newman algorithm (Despala-
tovi
´
c et al., 2014).
• Spectral clustering: This method uses the eigen-
vectors of the graph Laplacian matrix to embed
nodes in a lower-dimensional space and then ap-
ply clustering algorithms (Liu and Han, 2018).
• Hierarchical clustering: This approach creates a
hierarchy of clusters by iteratively merging or
splitting existing clusters (Bonald, 2018).
• Deep learning-based methods: Recent advances
in deep learning have led to the development of
graph neural networks (GNNs) for graph clus-
tering tasks. GNNs can learn representations of
nodes and edges that capture the underlying struc-
ture of the graph (Wu et al., 2020).
• K-means clustering: While not specifically de-
signed for graph clustering, K-means can be ap-
plied to the node embeddings obtained from graph
clustering algorithms to further refine the clusters
(Galluccio et al., 2012).
Network representation learning, also known as
network embedding, aims to learn low-dimensional
representations for nodes in a graph that capture the
underlying structure and relationships between nodes.
These representations can be used for various tasks,
including node classification, link prediction, and
community detection (Wang et al., 2022).
2.2 Trust and Reputation Assessment
Trust and reputation are fundamental concepts in
multi-agent systems, particularly in dynamic environ-
ments where agents interact, collaborate, and make
decisions based on their perceptions of each other’s
trustworthiness. Trust and reputation are essential
for effective collaboration and cooperation among
agents. (Drawel et al., 2022) explains the art of
Enhancing Graph Clustering in Dynamic Networks with Distributed Online Life-Long Learning
81

propagating trust in a scalable manner among the
agents. This lays the foundation on how the repu-
tation could be built over time through information
exchange. (Barbosa et al., 2023) significantly de-
scribes the importance of trust sharing in the negotia-
tion phase of agents to mitigate the malicious agents
in the network. (Khalid et al., 2021) introduces al-
gorithms to effectively validate the trust credibility of
agents as seen through the observers in the social net-
work.
2.3 Colluding Agents in Multi-Agent
Systems
Colluding agents in multi-agent systems pose signif-
icant challenges to trust and reputation systems. The
colluding agents form groups and communities to ma-
nipulate the trust scores of each other thereby cor-
rupting the overall reputation scores in the social net-
work. Some of the possible ways to detect such col-
luding agents include identifying abnormal patterns in
agent behavior (Johnson and Sokol, 2020), analyzing
the structure of agent relationships to detect cliques
or communities that might be engaged in collusion
(Mohanty, 2020) and employing machine learning al-
gorithms to learn patterns of collusion and identify
potential culprits (Rodr
´
ıguez et al., 2022). Detecting
collusion in dynamic environments can be challeng-
ing, as the patterns of collusion may evolve over time.
2.4 Integration of Graph Clustering
and Trust
Several studies have explored the integration of graph
clustering with trust and reputation systems. (Ros-
setti and Cazabet, 2018) reviews the idea of modeling
the evolution of dynamic network as nodes and edges
representing the agents and their interactions. These
studies often focus on static environments or do not
explicitly address the challenges of dynamic networks
that evolves over time. Our proposed approach, which
integrates DOL3 with graph clustering, offers a novel
solution to these challenges. The approach ensures
that the influence of the outdated information due to
the dynamic nature of the environment is addressed.
The graph clustering ensures that the model can iden-
tify the colluding agents to penalise them with lower
trust scores.
Life-long learning is a machine learning paradigm
where a model can continuously learn and adapt to
new data and tasks over time. This is particularly im-
portant in dynamic environments where the data dis-
tribution may change.
3 PROPOSED FRAMEWORK
Our proposed framework for trust and reputation as-
sessment in dynamic networks integrates Distributed
Online Life-Long Learning (DOL3) with graph clus-
tering. The framework consists of the following com-
ponents:
3.1 Agent Representation
Each agent is represented by a feature vector that
captures its characteristics and attributes. The fea-
ture vector ⃗x
i
of the i
th
agent can include information
such as the agent’s role, past behavior, reputation, and
other relevant features. The feature vector can be used
to carry the context of the interaction as well as the
belief of trust on other agents. Some of the character-
istics considered in this framework include:
• Behavioral data: Past actions, interactions, and
decisions.
• Reputation scores: Ratings or assessments from
other agents.
• Social connections: Relationships with other
agents in the network.
• Domain-specific features: Features relevant to the
particular application or domain.
By representing these characteristics in feature
vectors, we can apply machine learning algorithms
and data mining techniques to analyze agent behav-
ior, identify patterns, and make predictions about their
trustworthiness.
Let A be the set of all agents in an environment.
a
i
represents the individual agents. F is the set of
features characterising an agent. f
i j
be the specific
feature of the i
th
agent’s j
th
feature. Each agent can
be represented by a feature vector ⃗x
i
:
⃗x
i
= [ f
1
(a
i
), f
2
(a
i
),.., f
n
(a
i
)] (1)
where:
• n is the total number of features
• f
j
(a
i
) is the value of feature f
j
for agent a
i
3.2 Graph Construction
A graph G = (V, E) is constructed to represent the
relationships between agents. Vertex V in the graph
corresponds to set of agents which are represented by
nodes , and edge E represents connection or interac-
tion between agents. Edge weight w can be assigned
based on factors such as similarity, trust, or frequency
of interactions.
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82

Figure 1: Graph clustering integrated with DOL3 framework.
We used a directional graph to represent the
agents’ interactions among each other. This helps in
identifying the influence and community formation
among the agents. To represent the dynamic nature of
the environment, the overall graph G was simulated
to be random representing certain number of nodes
and edges. The edge weights also offer flexibility in
defining the algorithm by offering various character-
istics like:
• Frequency of Interactions: The number of times
agents have interacted.
• Reciprocity: Whether the relationship is mutual
or one-sided.
• Trust Levels: The level of trust between agents.
• Similarity: The degree of similarity between
agents’ features.
Edge weight function w(a
1
,a
2
) between two agents
/ nodes a
1
and a
2
can be defined using different func-
tions like Similarity-based for n features:
w(a
1
,a
2
) = sim(a
1
,a
2
) (2)
d(a
1
,a
2
) =
s
n
∑
i=1
(x
1
[i] − x
2
[i])
2
(3)
sim(a
1
,a
2
) =
1
(1 + d(a
1
,a
2
))
(4)
where sim(u,v) represents the similarity between
the two agents u and v. x
1
and x
2
represent the features
of a
1
and a
2
respectively. In this paper, all features
are represented numerically and hence the similarity
function with respect to euclidean function is consid-
ered. There are other similarity functions as defined
in (Onta
˜
n
´
on, 2020), but the Euclidean distance based
function is more appropriate for this specific use case.
Cluster modeling In the initialization phase, the
agents are assigned to their own clusters c
i
= {a
i
} for
i = 1, 2, 3..n. where n is the number of agents. During
the merging phase, the distance is calculated using (3)
between each pair of clusters. In Hierarchical Clus-
tering, even if a single point / feature is close to each
other between two clusters, its called Single-linkage
and Complete-linkage is when all the points are close
to each other. The single-linkage, complete-linkage
and average-linkage formulations are represented be-
low:
d(C
i
,C
j
) = min d(a
i
,a
j
)|a
i
∈ C
i
,a
j
∈ C
j
d(C
i
,C
j
) = max d(a
i
,a
j
)|a
i
∈ C
i
,a
j
∈ C
j
d(C
i
,C
j
) =
1
(|C
i
| ∗ |C
j
|)
∗
∑
d(a
i
,a
j
)|a
i
∈ C
i
,a
j
∈ C
j
(5)
Based on the type of linkage, the clusters C
i
and C
j
are merged into a new cluster C
k
.
Enhancing Graph Clustering in Dynamic Networks with Distributed Online Life-Long Learning
83

3.3 Distributed Online Life-Long
Learning (DOL3)
DOL3 enables agents to continuously learn and up-
date their models based on new information. Agents
maintain local models that are periodically updated
through a distributed consensus mechanism. The con-
sensus mechanism ensures that agents converge on a
shared understanding of the network and its dynam-
ics. As discussed in (Ramamoorthy et al., 2024),
DOL3 consists of four phases: Periodic reset (to han-
dle dynamic nature), Communication (Agents share
information), Trust Fusion (Weighted fusion of trust
rates with the neighbours) and Learning (update the
trust weights with decay). The periodic reset phase is
introduced in this framework to ensure non-stationary
nature is handled.
Data Collection and Update with Decay: in-
cludes agents continuously collecting information
about their interactions and relationships with other
agents as mentioned in the Section 3.2. This data can
include new edges, changes in edge weights, or node
attributes. As new data becomes available, agents up-
date their local clustering models. Assign weights to
new data points based on the chosen decay mecha-
nism.
In a dynamic social network, the evolution of
agents’ interaction is crucial in determining the collu-
sion behavior. We considered the decay mechanism
as stated by (Reitter and Lebiere, 2012) for updat-
ing the information about the social network at ev-
ery iteration. Decay mechanism is introduced into
the DOL3-based graph clustering framework to ad-
dress the potential influence of outdated information
and ensure that the system remains responsive to re-
cent changes. DOL3 iterations consist of the follow-
ing steps:
• Periodic Reset. Regularly reset the trust values to
a predefined baseline. This phase is implicitly in-
corporated into the trust update mechanism. The
α parameter in the trust update equation can be
adjusted to control the rate at which past informa-
tion decays. A smaller α will cause older informa-
tion to have less influence on current trust values,
effectively resetting trust over time.
T
i j
= T
i j
∗ (1 − α) + α ∗ B
0
(6)
In this formulation, the first term T
i j
∗ (1 − α) de-
cays the previous trust value over time, while the
second term α ∗ B
0
adds a portion of the baseline
trust value.
By adjusting the value of α and the baseline B
0
,
you can control the rate of decay and the level to
which trust values are reset. For example, a higher
α will result in a faster decay, while a higher B
0
will set the trust to a higher baseline value.
This formulation ensures that trust values are pe-
riodically reset to a predefined level, helping to
maintain the system’s responsiveness to chang-
ing conditions and preventing the accumulation of
outdated information.
• Communication. Agents exchange information
about their local models and observations. The
communication phase is reflected in the calcula-
tion of the weighted average in the global consen-
sus step. Agents exchange information about their
local models and trust values, which are then com-
bined to form the global consensus.
• Trust Fusion. Agents update their trust in other
agents based on the shared information and previ-
ous trust values. The trust fusion step is explicitly
represented in the equation for updating trust val-
ues:
T
i j
= (1 − ε) ∗ T
i j
+ ε ∗
∑
k∈N(i)
w
ik
∗ T
k j
(7)
This equation calculates the updated trust value
T
i j
based on the weighted average of the trust
values from neighboring agents a
i
and a
j
. The
first term (1 − ε) ∗ T
i j
represents the agent’s
own assessment of trust. The second term ε ∗
∑
k∈N(i)
w
ik
∗ T
k j
represents the influence of neigh-
boring agents on the trust value.
• Learning. Agents update their local models us-
ing the new data and the updated trust values. The
learning phase is incorporated into the model up-
date step: M
i
. f it(D
i
). This step updates the local
model M
i
based on the new data D
i
. The updated
model can then be used to make predictions and
influence the agent’s behavior. The learning phase
incorporates the decay functionality as mentioned
above.
T
i j
:= T
i j
∗ (1 − α) + α ∗ ∆T
i j
(8)
where ∆T
i j
is the change in trust between agents
a
i
and a
j
based on recent interactions or observa-
tions. The equation essentially updates the trust
value T
i j
by combining the previous trust value
with a weighted average of the recent change in
trust. The α parameter determines the balance be-
tween maintaining existing trust relationships and
incorporating new information.
3.4 Global Consensus
Agents periodically exchange their updated clustering
models with neighboring agents during the Trust fu-
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84

sion stage of DOL3 as mentioned in Section 3.3. A
consensus mechanism is used to combine these mod-
els into a global clustering solution. We propose a
weighted average approach based on the number of
shared edges:
C =
∑
i
w
i
∗ c
i
∑
i
w
i
(9)
where C is the global clustering solution, c
i
is the
local clustering model of agent a
i
, and w
i
is the weight
of agent a
i
in the consensus. Introducing the decay
mechanism during the Global consensus would im-
prove the framework’s responsiveness to the recent
changes in the network.
w
i
= α
(t − t
i
)
(10)
The Global consensus consists of three compo-
nents:
• Calculation of time difference: t −t
i
calculates the
time elapsed since data point i was observed.
• Exponential decay: The term α
(t − t
i
)
applies ex-
ponential decay to the weight. As time passes, the
exponent t −t
i
increases, causing the weight to de-
crease exponentially.
• Weight assignment: The calculated value is as-
signed to w
i
, effectively reducing the influence
of older data points on the clustering model.
The global consensus model represents a collective
view of the system, incorporating the knowledge and
insights from all agents. The weights assigned to in-
dividual agents reflect their relative importance in the
consensus process.
The DOL3 framework allows for continuous
adaptation to changing environments and the incor-
poration of new information.
4 EXPERIMENTAL SETUP
To evaluate the performance of our proposed frame-
work, we conducted a series of experiments using the
Mesa agent-based modeling framework. We simu-
lated a dynamic network environment where agents
represented nodes in a graph, and their interactions
were modeled as edges. We ran the experiment for
500 Monte Carlo simulations to provide more robust
result and quantify uncertainty. We used NVIDIA
RTX 4000 GPU with 3840 CUDA cores and 8GB
GDDR6 memory.
4.1 Hyperparameters and Initial Setup
The number of agents N in the simulation directly
affects the scale and complexity of the network. A
Figure 2: Class connectivity in Cora dataset.
larger number of agents can lead to more diverse in-
teractions and a richer dataset. We conducted the
study by varying the number of agents from 100 to
500. Network Topology plays a vital role on the
performance of the algorithm. The structure of the
network can influence the dynamics of agent interac-
tions and the formation of clusters (Kołaczek, 2010).
Different topologies, such as random graphs, small-
world networks, and scale-free networks, was ex-
plored to assess their impact on the results.
The initial trust values assigned to agents can af-
fect the starting point of the simulation. Random ini-
tialization or assigning initial values based on domain
knowledge is considered. For example, all the agents’
trust scores are initialised as 1, meaning fully trusted
in Step 1. The learning rate controls the speed at
which agents update their trust values. A higher learn-
ing rate can lead to faster adaptation but may also in-
troduce instability. Based on the studies conducted,
the learning rate (η) of 15 is considered for the exper-
iment. The decay factor (α) determines how quickly
past information is discounted. A higher decay fac-
tor can make the system more responsive to recent
changes, while a lower decay factor can preserve his-
torical information. We considered the decay factor of
α = 0.5. The choice of clustering algorithm can im-
pact the quality of the clustering results. Different al-
gorithms, such as Louvain Modularity Optimization,
spectral clustering, or hierarchical clustering, is evalu-
ated. We defaulted Louvain Modularity Optimization
for local clustering considerations.
4.2 Dataset
We used the Cora dataset (McCallum, 2024), a popu-
lar benchmark dataset for graph-based machine learn-
ing tasks. The Cora dataset consists of 2708 sci-
entific papers categorized into seven classes: Case-
based reasoning, Genetic Algorithms, Neural Net-
Enhancing Graph Clustering in Dynamic Networks with Distributed Online Life-Long Learning
85

Figure 3: Types of networks in Cora dataset.
works, Probabilistic Methods, Rule-Based Methods,
Theory of Computation, and Uncertainty. Each paper
is represented by a 1433-dimensional feature vector,
capturing the bag-of-words representation of the pa-
per’s content. Figure 3 illustrates the different types
of social networks in Cora dataset as identified during
the simulation. The dataset provides a well-defined
graph structure representing citation relationships be-
tween papers, which is similar to the dynamic net-
works in which our framework is intended to operate.
Figure 2 explains how the network types are ar-
rived at. The general patterns that are identified in-
clude:
• Intra-class Connectivity: Papers within the same
class are likely to have stronger connections than
papers from different classes. This is because pa-
pers on similar topics often cite each other more
frequently
• Inter-class Connectivity: There may be some con-
nections between papers from different classes,
especially if the topics are related or complemen-
tary.
• Hierarchical Structure: The class connectivity
might exhibit a hierarchical structure, with some
classes being more central or influential than oth-
ers.
4.3 Baseline Evaluation
The state-of-the-art models like hierarchical cluster-
ing, K-means clustering, spectral clustering and ER
EigenTrust based clustering are chosen based on the
literature surveys from (Nezamoddini and Gholami,
2022) and (Marciano, 2024) as mentioned in Section
2. These models are run against the simulated dy-
namic environment with Cora dataset.
Figure 4: Metric Result Analysis.
4.4 Evaluation Method
Larsen and Aone’s F Score was the evaluation method
used for comparing the clustering as refered by (John-
son et al., 2013). Since the Cora dataset already pro-
vides the labels which can be looked at as clustering,
the objective of the evaluation would be to check the
identical clustering output. An F score closer to 1
would mean that the clustering is identical. Higher
the F-Score, better the algorithm works in identifying
the colluding agents thereby penalising the malicious
agents.
Apart from the F score, we used the typical met-
rics like Normalized Mutual Information (NMI) to
measure the accuracy of the clustering results (New-
man et al., 2020). Convergence time was also used to
evaluate the performance of the algorithm along with
the usual metrics like precision and recall to evaluate
the performance of agent trust assessment and mali-
cious agent detection.
The F Score F(C,L) for the Class C and Label L
is calculated using the below equation:
F(C, L) = 2 ∗
P(C, L).R(C,L)
P(C, L) + R(C, L)
(11)
where P(C, L) and R(C,L) are the precision and
recall. This is the F Score for a specific label. For cal-
culating the FScore for the entire cluster, we ideally
take the weighted average over the labeling of every
class in the cluster.
4.5 Result
In this section, we present the result of running the
500 Monte Carlo simulations on Cora dataset with
manipulation of edges and vertices to simulate the dy-
namic environment. Table 1 gives the summary of the
metrics across each of the approaches. From Figure
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86

Table 1: Comparison of metrics on all approaches.
Approach NMI Recall Precision F1- Score Convergence Time (s)
Hierarchical Clustering 0.6 0.75 0.75 0.7 15
Spectral Clustering 0.76 0.85 0.83 0.84 20
ER EigenTrust 0.72 0.78 0.75 0.65 10
K-Means Clustering 0.70 0.75 0.73 0.74 5
DOL3 Enhanced Graph Clustering 0.85 0.88 0.87 0.88 25
4, it is clear that DOL3 based Graph Clustering ap-
proach outperforms the baselines in terms of NMI,
indicating better clustering accuracy. Spectral Clus-
tering is likely to perform well due to its ability to cap-
ture complex structures in the graph. ER EigenTrust
has lower performance due to its reliance on trust rela-
tionships and the potential for manipulation. The area
where DOL3 based approach under-performs is the
time it takes to converge on a consensus. Convergence
Time is expected to be higher for DOL3-Enhanced
Graph Clustering. This is due to the additional steps
involved in DOL3, such as trust fusion, learning, and
global consensus. These steps require iterative cal-
culations and communication between agents, which
can increase the computational overhead. From the
table 1, we could see that DOL3 integration improves
the accuracy by 11.8%. The formula that was used
to calculate was : Percentage Improvement = ((Ac-
curacy of our Approach - Accuracy of Best Baseline
(Spectral Clustering)) / Accuracy of Best Baseline) *
100
However, the trade-off is that DOL3 offers im-
proved adaptability and robustness, making it suitable
for dynamic environments where relationships and in-
teractions may change over time.
We extended this experiment to further test on
DOL3 based Graph clustering approach’s ability to
respond when the number of agents and the social
graph is changed over time. In addition to the evalua-
tion metrics mentioned in the Table 1, we introduced
further metrics to measure the performance of the al-
gorithms in dynamic environment. As seen in the re-
sult 5, the DOL3 based Graph Clustering approach
performs consistently over the time with number of
cluster changing along with the social graph.
The analysis of the Figure 5 and Figure 6 clearly
shows that the DOL3 algorithm demonstrated excep-
tional resilience in navigating dynamic network envi-
ronments. Its four-phase structure proved instrumen-
tal in swiftly adapting to system changes, outperform-
ing other algorithms that struggled to cope with the
uncertain number of malicious agents.
• Periodic Reset: This phase ensured that outdated
information was regularly discarded, allowing the
algorithm to remain responsive to evolving condi-
tions.
Figure 5: Dynamic Network F1 Score.
Figure 6: Dynamic Network Algorithm Resilience.
• Communication: Efficient communication be-
tween agents facilitated the rapid dissemination of
critical information, enabling timely updates and
adjustments.
• Trust Fusion: By carefully combining trust val-
ues from multiple sources, DOL3 mitigated the
impact of potential manipulation by malicious
agents.
• Learning: The continuous learning mechanism al-
lowed the algorithm to adapt its models to chang-
ing circumstances, ensuring its effectiveness in
dynamic settings.
It could be seen from the sharp down slides in Fig-
ure 6 that DOL3 based Graph Clustering takes very
minimal time to respond to dynamic evolution of the
network. In contrast, other algorithms often faced
challenges in handling the uncertainty associated with
fluctuating numbers of malicious agents. Their inabil-
Enhancing Graph Clustering in Dynamic Networks with Distributed Online Life-Long Learning
87

Figure 7: Impact of DOL3 on performance.
ity to adapt quickly to these changes hindered their
performance and compromised the system’s security.
4.6 Ablation Studies
We performed ablation studies to understand the im-
portance of some of the parameters in the DOL3
framework. The study included measuring cu-
mulative rewards (identifying non-malicious agents)
across 50 agents over several Monte Carlo simulation
runs. In each of the runs, the network social struc-
ture was changed at random to replicate a real-life
scenario.
4.6.1 Impact of DOL3
We compared the performance of our approach with
a variant that excluded the DOL3 component. Re-
sults showed that DOL3 significantly improved the
accuracy and adaptability of the system, especially in
dynamic environments. It is noticed that DOL3 can
help to reduce the impact of noise and uncertainty
in the data. By incorporating a learning rate and de-
cay factor, the system can gradually update its beliefs
based on new information, avoiding sudden changes
that might be caused by outliers or temporary fluc-
tuations. DOL3 can make the system more robust
to malicious agents and adversarial attacks. By con-
tinuously updating trust values and detecting anoma-
lies, DOL3 can help identify and mitigate the influ-
ence of malicious actors. This is evident from the
rate of climb of the cumulative reward as shown in the
Figure 7. Overall, the DOL3 component is essential
for the success of our proposed framework, providing
the necessary adaptability and robustness to address
the challenges of dynamic networks. By integrating
DOL3 with graph clustering and trust fusion, we are
able to create a more effective and reliable system for
trust and reputation assessment.
Figure 8: Impact of Graph Clustering on F1 score.
4.6.2 Impact of Graph Clustering
We compared the performance with a version that
did not use graph clustering. The results demon-
strated that graph clustering was crucial for identify-
ing meaningful communities of agents and improv-
ing the accuracy of trust and reputation assessment.
We compared the number of clusters remaining to
be merged over the period of time between a non
graph clustering technique like ER EigenTrust with
the Graph clustering approach. While Graph Clus-
tering can reveal hidden patterns through the net-
work structure, ER EigenTrust method depends on the
trust recommendation from other agents. ER Eigen-
Trust seemed to be extremely vulnerable to noise and
manipulations from malicious agents. We simulated
more clusters and compared the number of clusters to
be merged with the F1 score at that point in time. It is
seen that the trend on the F1 score remains exactly the
same. However, the Graph based clustering has bet-
ter F1 score through out compared to ER EigenTrust
as seen in the Figure 8. Graph clustering is gener-
ally a more effective approach for identifying com-
munities and assessing trust in complex networks, as
it directly analyzes the structural properties of the net-
work rather than relying solely on recommendations.
However, the choice between graph clustering and ER
EigenTrust may depend on the specific characteristics
of the network and the desired outcomes.
4.6.3 Impact of Trust Fusion
Trust Fusion is an important phase in DOL3 frame-
work as mentioned in the Section 3.3. The agents
consider the neighbouring agents’ trust values over
weights to finalise the own assessment. We performed
ablation studies to check on the impact of not hav-
ing the trust fusion in the DOL3 framework. As seen
in the Figure 9, the key benefits of Trust Fusion in-
cludes reduced uncertainty, improved accuracy and
faster adaptability. During this ablation study, we rec-
ognized that trust may be context-dependent, and dif-
ferent factors may influence trust in different situa-
tions. Considering the context while sharing the fea-
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88

Figure 9: Impact of Trust Fusion on cumulative reward.
Figure 10: Impact of Global Consensus on Similarity func-
tion.
ture information would have more closer trust value
than the one without context.
4.6.4 Impact of Global Consensus
Global consensus, the process of aggregating the lo-
cal models of individual agents into a shared under-
standing, is another critical component of our pro-
posed framework. It plays a significant role in en-
suring consistency, coherence, and accuracy in trust
and reputation assessment. Some of the key benefits
of Global Consensus includes:
• Consistency: Global consensus helps to ensure
that agents have a consistent understanding of the
network and its dynamics. This can prevent in-
consistencies and conflicts in decision-making.
• Coherence: By combining the insights from mul-
tiple agents, global consensus can provide a more
coherent and comprehensive view of the network.
• Accuracy: Global consensus can improve the ac-
curacy of trust and reputation assessments by
leveraging the collective knowledge of the system.
• Resilience: Global consensus can make the sys-
tem more resilient to the influence of individual
outliers or malicious agents.
• Scalability: Global consensus can be applied to
large-scale networks, as it allows for distributed
processing and information sharing.
To understand the consistency, the similarity func-
tion mentioned in the equation (4) is considered.
This exhibits the similarity among the agent’s features
thereby measuring the clustering among the agents
group.
From the Figure 10, it can be seen that the system
exhibits consistency when Global Consensus is con-
sidered in the framework.
5 CONCLUSION
We have demonstrated on how to solve the collusion
problem in Multi-Agent system in a dynamic environ-
ment. While the DOL3 integrated Graph based clus-
tering approach takes more computation cycles, the
trade off with regards to stability, performance and
resilience is more. Our experimental results demon-
strate the superior performance of our approach com-
pared to traditional methods, particularly in terms of
accuracy, adaptability, and robustness. The DOL3
framework effectively addresses the challenges of dy-
namic environments by enabling agents to continu-
ously learn and update their models.
Graph clustering provides a valuable tool for iden-
tifying communities of agents and assessing their
trustworthiness. The combination of DOL3 and graph
clustering offers a robust and scalable solution for
trust and reputation assessment. Our approach out-
performs traditional methods in terms of accuracy,
particularly when dealing with dynamic networks and
changing agent behaviors.
One of the topics that is not considered in this
paper is that of sharing the context while identify-
ing the malicious agent. The future direction would
be to explore techniques for incorporating contex-
tual information into the consensus mechanism to im-
prove the accuracy and relevance of the global model.
One of the possible approaches could be to extend
the feature vector to include the context without los-
ing the privacy on sharing the information with other
agents. Another future direction would be to inves-
tigate methods to optimize the computational com-
plexity of the algorithm, particularly for large-scale
networks. We could also possibly extend the study
to improve the computational efficiency through par-
allel and distributed implementations. We could also
explore contextual trust fusion process to make more
informed decisions.
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