Attributed-based Label Propagation Method for Balanced

Modularity and Homogeneity Community Detection

Jenan Moosa

, Wasan Awad

and Tatiana Kalganova

College of Information Technology, Ahlia University, Manama, Bahrain

College of Engineering, Design and Physical Sciences, Brunel University, London, U.K.

Keywords: Community Detection, Label Propagation, Homogeneity, Covid-19, Modularity.

Abstract: Community Detection is an expanding field of interest in many scopes, e.g., social science, bibliometrics,

marketing and recommendations, biology etc. Various community detection tools and methods have been

proposed in the last years. This research is to develop an improved Label Propagation algorithm (Attribute-

Based Label Propagation ABLP) that considers the nodes’ attributes to achieve a fair Homogeneity value,

while maintaining high Modularity measure. It also formulates an adaptive Homogeneity measure, with

penalty and weight modulation, that can be utilized in consonance with the user’s requirements. Based on the

literature review, a research gap of employing Homogeneity in Community Detection was identified, and

accordingly, Homogeneity as a constraint in Modularity based methods is investigated. In addition, a novel

dataset constructed on COVID-19 contact tracing in the Kingdom of Bahrain is proposed, to help identify

communities of infected persons and study their attributes’ values. The implementation of proposed algorithm

performed high Modularity and Homogeneity measures compared with other algorithms.

1 INTRODUCTION

Extensive research was done to detect communities

within networks, detected communities are densely

connected nodes that are strongly connected to each

other in or the subnetwork (community) than to the

rest of the network(WU et al., 2020). In social

networks, a community can be defined as a group of

nodes or persons that are similar to each other and

dissimilar from the rest of the group (Raghavan et al.,

2007). This indicates that the group of nodes in one

community will most likely share the same

characteristics or interests. Whereas in attributed

networks, the nodes in a community will most likely

share the same attributes’ values.

To assess the output of generated communities,

different number of measures are being used,

including Modularity measure which indicates the

quality of the generated partitions or communities.

However, the integration of different types of

constrains or external information on community

composition was rarely investigated (Viles &

https://orcid.org/0000-0002-9081-7748

https://orcid.org/0000-0001-7152-3480

https://orcid.org/0000-0003-4859-7152

O’Malley, 2017), and Homogeneity as constraint still

remains uncharted. In consequence, the detected

communities might contain irrelevant nodes in one

cluster even-though the communities scored a good

fitness score in other measures such as Modularity.

To overcome this, a Homogeneity measure can be

integrated with Modularity, to consolidate the

evaluation process. So, a method that maximizes both

Modularity and Homogeneity is proposed, with

Modularity and Homogeneity as objective functions.

On the other hand, as constrained community

detection shows robust performance on noisy data

since it uses background knowledge(Nakata &

Murata, 2015) and the restriction of the type

considered here has, to our knowledge, remained

unstudied, Modularity with Homogeneity as a

constraint is also tested to adjust the detection of

homogenous communities.

The scientific contributions of this paper are:

1. Develop an Attribute-Based Label

Propagation algorithm that considers the

nodes’ attributes to achieve a fair

Moosa, J., Awad, W. and Kalganova, T.

Attributed-based Label Propagation Method for Balanced Modularity and Homogeneity Community Detection.

DOI: 10.5220/0010928200003116

In Proceedings of the 14th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2022) - Volume 3, pages 905-912

ISBN: 978-989-758-547-0; ISSN: 2184-433X

905

Homogeneity value, while maintaining a high

Modularity measure.

2. Formulate an adaptive Homogeneity measure,

with penalty and weight modulation, that can

be utilized based on the user’s requirements.

3. A research gap of employing Homogeneity in

Community Detection was identified, and

accordingly, Homogeneity as a constraint in

Modularity based methods is investigated.

4. Design a novel dataset based on COVID-19

contact tracing in the Kingdom of Bahrain, to

help identify communities of infected persons

and study their attributes’ values.

2 RELATED WORK

Effective community detection is an important tool

for analyzing networks; it provides thorough

knowledge of the network, in addition to the structure

and functional characteristics of the network (WU et

al., 2020). Community detection problem is getting

more attention, as different algorithms and techniques

have been proposed, which includes traditional

algorithms (Fortunato, 2010)(Shen et al., 2009),

evolutionary algorithms (Karimi et al., 2020)(N.

Chen et al., 2020), heuristic (Clauset et al., 2004;

Sobolevsky et al., 2014) hierarchical clustering (Lu et

al., 2015) , spectral clustering (Luxburg, 2007), label

propagation (Raghavan et al., 2007), neural networks

(Bruna, 2017), etc.

2.1 Evaluation Measures

The detected communities are evaluated using a

number of evaluation measures such as Modularity

(M. E. J. Newman & Girvan, 2004), which measures

the fraction of the edges in the network that connect

vertices of the same type (i.e., within-community

edges) minus the expected value of the same quantity

in a network with the same community divisions but

random connections between the vertices. Modularity

has been used to compare the quality of the partitions

obtained by different methods, but also as an

objective function to optimize (M. Newman, 2003).

Homogeneity was also used as an objective

function (Wu & Pan, 2016), a measure was proposed

based on Shannon information entropy theory in

which the entropy of a set, measures the average

Shannon information content of the set.

Unfortunately, the modularity values produced in this

research were significantly lower than others.

Moayedikiaa (Moayedikia, 2018) used the

proposed Homogeneity in (Wu & Pan, 2016) as an

objective function by developing an attributed

community detection algorithm wrapped by

Harmony Search that relies on nodes’ importance to

form communities. Yet this algorithm performed a

long execution time, and it also suffered from

entrapment in local optima. Another research

proposed a method for community detection based on

a higher-order feature termed Attribute Homogenous

Motif (P. Li et al., 2018), which integrates both node

attributes and higher-order structure of the network.

However, the modularity was neglected in this

research.

The evaluation measures used can assess one

criterion only, so different measures are used to

evaluate different aspects of the result. As one method

might generate results that perform well in one

evaluation measure while fail to achieve a fair result

in another one. Thus, an evaluation technique that

takes this issue into account needs to be studied.

2.2 Community Detection with

Constraints

Constrained community detection approaches are

used to take advantage of the existing side

information of the network (Ganj et al., 2018). This

aids in generating more efficient and actionable

results, and help develop data mining techniques that

can handle complex and domain-specified constraints

(Ganji et al., 2017). Table 1 presents several

constrained community detection methods, along

with the evaluation measure used to evaluate the

results.

Table 1: Community detection with constraints.

Paper Method Constraints Objective function

(Ganj, Bailey

and Stuckey,

2018)

Lagrangian

Constrained

Must-Link,

Cannot-Link

Normalized Mutual

Information,

Noise Sensitivit

(Ganji, Bailey

and Stuckey,

2017)

Programming

modelling technology

Global,

Community and

Instance level

Normalized Mutual

Information,

Modularity, Run-Time

(Chin and

Ratnavelu,

2017)

Label propagation

algorithm with

constraints

Propagating

labels,

Communities’

Exemption

Normalized Mutual

Information,

Modularity

(Chin and

Ratnavelu,

2016)

Constrained Label

Propagation Number of links

of a node to the

nodes in a

community

Normalized Mutual

Information,

Normalized Variation

Information,

Modularity,

Modularity density

Most of the current community detection methods

consider the structural information of networks, but

disregard the fruitful information of the nodes, and this

results in the failure of detecting semantically

meaningful communities (P. Li et al., 2018). However,

Homogeneity was never studied as a constraint, and

was always treated as an objective function.

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The two objective functions (Modularity and

Homogeneity) are conflicting, which means that

improving one of them leads to degradation of

another (Moayedikia, 2018). Modularity has proven

its effectiveness in evaluating community detection

problem, many algorithms are based on modularity

maximization (Tsung et al., 2020). Hence comes the

idea of testing the Homogeneity as a constraint, in

addition to testing it as an objective function. As

constrained algorithms are effective in dealing with

combined optimization problems, due to its wide

representation scope and generally applicable solving

methods(Y. C. Chen et al., 2010).

3 PROPOSED METHODS

In this section, new Attribute-Based Label

Propagation (ABLP) algorithms based on attributes’

regulation are proposed.

3.1 ABLP Algorithm

The proposed method is an Attribute-Based Label

Propagation Algorithm is a Modularity maximization

based on Label Propagation algorithm with regards to

homogeneity. As Label Propagation is considered as

one the effective algorithms amongst the existing

algorithms used for community detection because of

its time efficiency (Chin & Ratnavelu, 2017).

Algorithm 1: ABLP.

The concept of the algorithm is based on

examining the neighbors of the node in the network.

Each node (x) will be labeled with a number that

indicates its community. First each node will have a

unique label, and then the labels will propagate

throughout the process. The label of x will be changed

based on its neighbors’ labels. Node x will also check

the attribute of its neighbor, nodes with similar

attributes will most likely have the same label. This

step will be iterated, and each node will update its

label at every step, the node will get the label that the

maximum number of neighbors carry. Finally, x will

join the community that contains most of his

homogeneous neighbors. In this way, ABLP

algorithm tries to maximize Modularity and

Homogeneity at the same time.

3.2 Constrained ABLP Algorithm

The same concept of the proposed ABLP is followed,

with regards of homogeneity as a constraint, which

penalizes the Modularity measure by minimizing it

based on the achievement of the homogeneity value.

So ideally, if the homogeneity degree is high, the

modularity measure should remain at its best.

However, if the homogeneity degree is low, the

Modularity value should be punished and reduced.

Algorithm 2: Constrained ABLP.

The Constrained Attribute-Based Label

Propagation algorithm is a highest-modularity,

homogeneity constraint-satisfying solution for the

community detection problem in attributed networks.

The algorithm considers the run that generates the

maximum constrained Modularity and proposed

measure of Penalized Homogeneity degrees.

4 PROPOSED EVALUATION

MEASURE

In this section, Homogeneity Degree that considers

the networks’ structure, in addition to a Penalized

Homogeneity measure are proposed. These measures

will later be used to evaluate a number of social

networks in the community detection problem.

Attributed-based Label Propagation Method for Balanced Modularity and Homogeneity Community Detection

907

4.1 Evaluation Measures

Homogeneity in community detection was first

proposed by (Wu & Pan, 2016), it was defined based

on Shannon information entropy theory, the entropy

of a set measures the average Shannon information

content of it. This homogeneity measure considers the

proportion of the number of nodes with a certain

attribute in a community to the total number of nodes

in a community. The measure does not consider the

network structure, as real-world datasets might have

some aspects that need to be considered.

As homogeneity was used as an objective

function to measure the homogeneity of the detected

communities in the network as one unit, here is the

proposal of a new of homogeneity measure that

evaluates the homogeneity degree in each

community, based on specified attribute values.

The formula will calculate the number of nodes

with the specified attribute divided by the total

number of nodes in the cluster. It reflects the standard

deviation; however, standard deviation finds how

concentrated the data is around the mean, in our case,

the mean will be ignored, µ=0;

The closer the value is to 1, the more

homogeneous the cluster is. This can be calculated in

𝐻𝑐



which is the Homogeneity of community k.

Hd =

















(1)

Where Hd

is the average Homogeneity degree in

the Communities: att is the number of attributes in the

network, n

att

is the number of nodes with each

attribute in a community, and N is the total number of

nodes in the community. The square value is

calculated as it adds more weighting to the

differences which makes the value more significant.

4.2 Penalized Homogeneity Degree

It should be noted that the Homogeneity degree (Hd)

measure proposed in section 4.1

does not consider the

number of communities and number of nodes in each

community compared to the total number of nodes in

the network. To add more flexibility and user-

preference to the proposed measure, a penalty will be

given, to ensure that nodes among all detected

communities are homogeneous, and that distribution

is fair.

To add more restrictions to the homogeneity

degree, we consider (P), a penalty that takes the

number of nodes for each attribute in the community

compared to the total number of nodes with this

attribute in the network.

P=1−



𝑛

()



(2)

Where n

att

is the number of nodes with each

attribute in a community, and N

att

is the number of

nodes with this attribute in the network, for the

attribute that owns the maximum number of nodes in

each community.

PHd= Hd - P

(3)

Where PHd measures the Penalized Homogeneity

Degree. This allows the user to apply an impartial

penalty for algorithms that detect a large number of

communities that contain a small number of nodes

with a certain attribute. It is also possible to set a

weight for the penalty, and consider more attribute,

based on the user’s requirement of how important

each attribute is.

MAWPHd= Hd - P∗𝑤 Hd − (P



∗𝑤







)

(4)

Multi-Attribute Weighted Penalized

Homogeneity degree can be calculated using the

MAWPHd measure. Where z is the number of

attributes to be considered, and w is the weight of

penalty to be applied.

On the other hand, to calculate Modularity

constrained by Homogeneity, the Penalized

Homogeneity Degree will be subtracted from 1 to

minimize the penalty of constraint. Because the

higher the Homogeneity value, the less punishment is

applied on the Modularity.

Q(C: H) =

|Q-1- Penalized Homogeneity Degree | (5)

Where Q(C: PHd) calculates the Modularity with

Penalized Homogeneity as Constraint, Q represents

Modularity, H is the Homogeneity (can be Hd

or PHd,

based on the experiment, dataset or research

requirements).

The proposed measures of (PHd) and

(MAWPHd) allow a more flexible mensuration of

Homogeneity on different types of attributed

networks, based on the user-defined requirements.

5 RESULTS AND DISCUSSION

In this section, the algorithm will be implemented on

two datasets in addition to a proposed dataset of

COVID-19 contact tracing. The results will be

compared to several existing algorithms. And then

will be compared in term of Modularity, and the

proposed measures of Homogeneity.

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5.1 Datasets

The datasets used for the experiments are attributed

social networks from the literature, in addition to a

proposed real-world dataset based on the contact

tracing of COVID-19 infected persons in the

Kingdom of Bahrain.

1 Political Books (PolBooks) a social network

consists of nodes representing books about US

politics. Edges represent frequent co-purchasing of

books by the same buyers. Books were labelled by

Newman (M. E. J. Newman, 2006) with an attribute

describing their political alignments. It consists of

105 nodes, and 441 edges (Figure 1).

Figure 1: US Political books network (Triangles: neutral,

dots: conservative, and squares: liberal) (Q. Wu et al., 2013).

2 American College Football network, represents

the games between Division IA colleges during

regular season fall in 2000 (Girvan & Newman,

2002). It consists of 115 teams and 613 games,

divided into 12 conferences (Figure 2).

Figure 2: American College football network (each team is

represented by a different color) (Binesh & Rezghi, 2018).

3 Proposed Dataset: COVID-19 Contact

Tracing: The COVID-19 pandemic has been termed

as the most consequential global crisis since the

World Wars. Because of the rapid prevalence of this

virus, health organizations all over the world tend to

track and store all data related to this pandemic. This

includes the contact tracing, number of cases, number

of deaths, etc. The availability of rich textual data

from various online sources can be used to understand

the growth, nature and spread of COVID-19(Usman

et al., 2020). According to World Health

Organization (World Health Organization, 2021),

contact tracing is the process of identifying,

assessing, and managing people who have been

exposed to a disease to prevent onward transmission.

When systematically applied, contact tracing will

break the chains of transmission of an infectious

disease and is thus an essential public health tool for

controlling infectious disease outbreaks. When contact

tracing data is compiled it can be represented by a

network, and hence structured into a graph, which can

be analysed using graph mining techniques.

As any network can be outlined in a graph, and

the graph is composed of a set of nodes which can be

individuals or entities, and edges that represent the

connections and interactions between the nodes(Bedi

& Sharma, 2016).

A dataset was proposed in (Moosa et al., 2021), it

is based on the spread of virus between countries. An

open-source contact tracing data was used to follow

the spread of virus from January to March 2020,

between the countries worldwide, which started in

China and expanded to other countries. Each country

is represented by a node, and an edge is used when a

country has a contact infected person from another

country. Unfortunately, this dataset cannot be used in

this research as it is not attributed network.

The data used to form this dataset was available

on Bahrain’s Ministry of Health website, and was

publicly available, it contained the contact tracing of

citizens who were infected by the COVID-19 virus,

the details include the case number, age, nationality,

gender, travel history (if any), and the other case

number contacted which caused the infection. Since

the data was publicly available on the website and it

does not contain any personal information which

makes it impossible to recognize any of the cases, it

did not require any ethical approval. The cases cover

the period 01/April/2020 to 10/May/2020.

Figure 3: Proposed Dataset: COVID-19 contact tracing in

the Kingdom of Bahrain.

The dataset consists of 750 cases represented by

nodes and 589 relationships between the cases

(contacted persons) represented by edges. Other cases

were ignored as the source of getting the virus was

unknown as they were tested as part of a campaign to

obtain random samples from the community or tested

positive after developing symptoms without clear

idea of the contacted persons.

Attributed-based Label Propagation Method for Balanced Modularity and Homogeneity Community Detection

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5.2 Experiments of Work

The proposed ABLP algorithm, along with several

existing algorithms will be implemented. The

algorithms used for comparison are:

- Asynchronous Label Propagation (LPA)

(Raghavan et al., 2007)

- Graph Embedding with Self Clustering

(GEMSEC) (Rozemberczki et al., 2019)

- An Edge Enhancement Approach for Motif-

aware (EdMot) (P.-Z. Li et al., 2019)

- Deep Autoencoder-like Nonnegative Matrix

Factorization (DANMF) (Ye et al., 2018)

5.3 Results

The main purpose of proposing the algorithm is to

maximize homogeneity, while maintaining a high

Modularity value. So, the Homogeneity degree will

be calculated and compared as an objective function.

And then the results will be tested again with

consideration of Homogeneity as a constraint.

5.3.1 Homogeneity as an Objective Function

It is observed that considering the nodes’ attributes

values will result in more homogeneous

communities. Nodes with similar attributes are

beyond any doubt share the same value, however,

they may not necessarily be neighbours or share

direct ties. So, paying more attention to the node’s

values helps detect denser communities in terms of

interests or preferences.

The results are shown in Tables 1,2,3 and 4. Where

Hd states the proposed Homogeneity measure in

detected communities (equation 1), P is the proposed

penalty measure (equation 2) and PHd is the proposed

Penalized Homogeneity degree values (equation 3).

Table 1: Results on Books Dataset.

As seen in Table1, the highest modularity value

was achieved in Books dataset by the proposed

Attribute-Based Label Propagation algorithm with a

value of 0.527, followed by EdMot algorithm with a

value of 0.5092.

As for the Homogeneity degree (before applying

the penalty), LPA achieved a high rate, however its

penalty was high because it detected two small

communities with node sizes 4 and 3, and all nodes in

both communities had the same attribute value. This

resulted in a high penalty and therefore a very low

penalized homogeneity degree. GEMSEC also had an

elevated penalty value for the same reason. This gives

rise to ABLP algorithm achieving the highest

assessment value among all other algorithms.

The Modularity measure values of American

College Football dataset were likely close by the expe-

rimented algorithm. However, Homogeneity measure

was significantly low as the communities detected

included nodes from diversified conference values.

Table 2: Results on Football Dataset.

For a higher homogeneity value, the community

should contain nodes with the least number of

attribute values possible. To better understand what

happened, the average number of attribute values in a

community can be calculated, and obviously, the

closer the value to 1, the better.

In American College football dataset, the number

of attribute values is 12, which can be considered high

to some extent compared to Books dataset which

consisted of 3 attribute values. It was observed that

when a community consists of nodes with more than

3 different attribute values, the homogeneity value is

relatively low. To prove this, a measure of Average

Attribute value (AAv) in a community is proposed

and calculated, as seen in Table 3. It can be clearly

perceived that higher Average Attribute value result

in higher penalty and thus a lower PHd value. This

draws a conclusion, that having multiple attribute

values in one community results in a non-

homogeneous environment.

Table 3: The average number of attribute value.

As for the proposed dataset, since it is a real-

world contact tracing network, and the number of

edges is less than the number of nodes, so the penalty

will not be considered as the nodes did not have

enough connections with one another.

The highest modularity value was again achieved

by the ABLP followed by EdMot. As well as the

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Table 4: Results on Proposed dataset.

homogeneity value which was the highest in the

proposed measure and the Label Propagation

Algorithm. It is also noticeable that while Edmot

achieved a high modularity value, it scored a

comparatively low homogeneity measure. As for

GEMSEC and DANMF, both algorithms detected a

low number of communities with high number of

nodes in one community, then divided the rest of the

nodes on the remaining communities. This manifestly

resulted in a low modularity value as well as a low

homogeneity measure.

5.3.2 Homogeneity as Constraint

Here the homogeneity is treated as a constraint, which

minimizes the Modularity value based on the

achievement of the homogeneity value. When the

Homogeneity value is high, modularity measure

should remain at its best. On the contrary, when the

value of Homogeneity is low, the Modularity value

should be punished and reduced. This is tested with

the same experiments, as seen in Table 5 and 6.

Where Q(C: H) is the value of Modularity constrained

with Homogeneity (equation 5). For Books and

Football datasets, PHd Homogeneity value is

considered since a penalty was applied.

Table 5: Homogeneity as constraint in Books dataset.

Table 6: Homogeneity as constraint in Football dataset.

And as the proposed COVID-19 dataset did not

need the penalty measure, the value of constrained

Homogeneity will be Hd.

Testing the homogeneity as a constraint helps in

evaluating the results in terms of Modularity and

Homogeneity at the same time. Here is it assumed

that both measures have the same importance or

Table 7: Homogeneity as constraint in proposed dataset.

weight in the results. However, a weight can be

assigned to the measures based on how important

each measure is. This will facilitate in the evaluation

process based on the defined user requirements,

which are aligned with the dataset itself. So, if the

user is interested more in the Homogeneity than

Modularity, a ratio of 70/30 can be applied, where

Homogeneity is responsible for 70% of the measure

and the Modularity is for the other 30%. This can be

calculated as |1- (0.3 * Q – 0.7 *H). In other words,

this way can be personalized according to the nature

of the dataset and the expected detected communities.

6 CONCLUSION

Community detection in attributed networks can be

evaluated in many aspects. The mostly used

evaluation measures such as Modularity, cannot

address the evaluation of Homogeneity. Hence,

Attribute-Based Label Propagation ABLP algorithm,

that considers the attribute values of nodes while

maintaining a high Modularity, and Homogeneity and

values is proposed. And to support evaluating the

proposed algorithm, an adaptable homogeneity

measure is also proposed. This measure assesses the

homogeneity in an attributed network and can be

penalized based on the type of the dataset.

Experiments on existing social networks were

conducted as well as on the newly proposed COVID-

19 dataset which is based on the contact tracing of the

virus infected persons in the Kingdom of Bahrain.

The algorithm appears to have good results in terms

of the discussed evaluation measures. As future work,

we tend to study the attribute consideration on the

familiar community detection algorithms.

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