BSODCS: Bee Swarm Optimization for Detecting Community Structure

Narimene Dakiche

Laboratoire des Methodes de Conception de Syst

emes (LMCS), Ecole Nationale Sup

erieure d’Informatique (ESI),

BP 68M - 16270 Oued Smar, Alger, Algeria

Keywords:

Social Networks, Community Detection, Bee Swam Optimization, Modularity.

Abstract:

This paper presents, BSODCS, a Bee Swarm Optimization for detecting community structure within networks.

It employs artiﬁcial bees to explore a search space and construct solutions for community detection. To

accommodate the speciﬁc features of networks, we adopt a locus-based adjacency encoding scheme. Each bee

makes decisions regarding its neighboring solutions and shares information through a dance. To explore the

neighborhood of each bee, we use Pearson’s correlation as the heuristic information. The modularity of the

bees’ solutions serves as a metric for evaluating their quality. The algorithm is tested on well-known real-world

networks, and the experimental ﬁndings demonstrate that BSODCS outperforms other existing swarm-based

methods, delivering higher-quality results.

1 INTRODUCTION

Modern network science has made signiﬁcant

progress in modeling complex real-world systems.

One key characteristic of these networks is the pres-

ence of community structure. Over the past few years,

numerous algorithms for community detection have

been proposed to uncover the structural properties and

collective behaviors in networks (Bedi and Sharma,

2016).

Community detection refers to the procedure of

dividing a network into groups of interacting nodes

depending upon their structural properties (Yang

et al., 2013). It has been proven to be an optimization

problem, considered NP-Hard, which involves maxi-

mizing various interesting objective functions (Bran-

des et al., 2007).

Modularity (Newman and Girvan, 2004) is by far

the most used and best known quality function for

measuring the quality of a partition of a network, even

thought it presents a resolution limit problem in cer-

tain realistic situations (Fortunato and Barth

elemy,

2007). Consequently, several community detection

algorithms are proposed to optimize it.

Swarm Intelligence is the ﬁeld of studying and de-

signing well-organized computational intelligent in-

teractive solutions, in which complex problems are

being solved by using the behavior of living swarms

such as birds, reptiles, ﬁsh, and ants (Nayyar et al.,

https://orcid.org/0000-0003-2371-616X

2018). Many swarm based optimization algorithms

have been adopted to tackle the community detection

problem.

Cai et al. (2014) introduced a discrete Particle

Swarm Optimization (PSO) algorithm speciﬁcally de-

signed for detecting communities in signed networks.

The same corresponding author further extends this

research in (Cai et al., 2015), focusing on the cluster-

ing of large-scale social networks.

Ant Colony Optimization (ACO) has gained

prominence as an effective global search meta-

heuristic for graph-related problems. Various adap-

tations of the ACO algorithm have been proposed for

community detection. Noteworthy instances of these

adaptations can be found in the works cited as (Chen

et al., 2012) and (He et al., 2011).

In recent times, researchers have begun to investi-

gate the applicability of contemporary nature-inspired

meta-heuristics for community detection. One of

these methods is Bat algorithm (BA), as demonstrated

in studies such as (Hassan et al., 2015) and (Song

et al., 2016). These works shed light on the effec-

tiveness of BA in tackling the community detection

problem in graphs.

Another notable adaptation for community de-

tection problems is the utilization of Fireﬂy Algo-

rithm (FA). Jaradat et al. (2018) present an interesting

study where a FA-based solver outperforms other bio-

inspired solvers, such as Genetic Algorithm (GA) and

Ant Colony Optimization (ACO), when applied to a

422

Dakiche, N.

BSODCS: Bee Swarm Optimization for Detecting Community Structure.

DOI: 10.5220/0012209300003584

In Proceedings of the 19th International Conference on Web Information Systems and Technologies (WEBIST 2023), pages 422-428

ISBN: 978-989-758-672-9; ISSN: 2184-3252

small set of real-life networks.

Artiﬁcial Bee Colony (ABC) is another contem-

porary bio-inspired solver that has been successfully

applied to community detection problem. In (Hafez

et al., 2014), an ABC based algorithm is introduced,

which autonomously determines the optimal number

of partitions in the network. Moreover, (Dakiche

et al., 2022) is an additional work that demonstrates

the effectiveness of ABC for community detection

challenges and offers insights into its potential appli-

cations in this domain.

Over the past decade, numerous algorithms in-

spired by the behavior of bees have been proposed

and applied to various problems (Karaboga and Akay,

2009). One such algorithm is Bee Swarm Optimiza-

tion (BSO), introduced as a metaheuristic by Drias

et al. (2005), which draws inspiration from the for-

aging behavior of real bees.

BSO is an effective approach that has demon-

strated promising results in several issues, such as sat-

isﬁability (Djeffal and Drias, 2013), association rules

(Djenouri et al., 2013), clustering (Sadeg and Drias,

2007), and feature selection (Sadeg et al., 2015). Due

to its effectiveness for those problems, we are inter-

ested in investigating its capabilities for community

detection problem.

To the best of our knowledge, only one study pur-

ported at proposing an algorithm based on BSO for

community detection problem (Belkhiri et al., 2017).

In their algorithm, the authors take modularity Q as

objective function and choose a string based schema

to represent the solutions. No explicit local search

was adopted to visit the solutions’ neighborhood ex-

cept for a ﬂipping algorithm to determine the search

area.

In our study, we propose to adapt the BSO algo-

rithm for community detection problem by using the

locus-based adjacency representation to record each

solution representing a community structure, which

has the advantage of enabling the algorithm to de-

tect communities’ number automatically, contrarily to

the string based representation. Moreover, while ex-

ploring each bee’s neighborhood, we propose to use

the network knowledge to select the most appropriate

neighbor. For that, we employ Pearson’s correlation,

which is a similarity measure between nodes. The al-

gorithm, we call BSODCS (BSO for Detecting Com-

munity Structure), reaches better modularities com-

pared to the ﬁrst-proposed BSOCD (Belkhiri et al.,

2017) and other swarm based algorithms from the lit-

erature.

The rest of the paper is organized as follows: In

sections 2, the commuity detection as an optimiza-

tion problem is described. In section 3, the general

algorithm of BSO is presented and its application for

community detection is described. Section 4 shows

the results of BSODCS and compares them to the re-

sults of other methods before we conclude with ﬁnal

remarks and directions for future works in section 5.

2 COMMUNITY DETECTION

PROBLEM

A complex network can be represented as a graph

G = (V,E), where V denotes the set of nodes and

E denotes the set of edges. The graph consists of

N = |V | nodes and m = |E| edges. To describe the

network, an adjacency matrix A of size N × N can

be used. Each element A

i j

in the matrix corresponds

to the presence (A

i j

= 1) or absence (A

i j

= 0) of an

edge between the i

and j

nodes. The ﬁnal com-

munity structure P = {C

,...,C

} of the network

is deﬁned, where each C

(l = 1,2,...,k) is a subset of

V , and k represents the total number of communities.

Community detection as an optimization problem

requires the use of an objective function to guide the

search for optimal solutions. The objective function

acts as the ”steering wheel” in the process, leading to

favorable solutions. The most widely used and well-

known quality function for evaluating the quality of a

network partition is modularity Q (Newman and Gir-

van, 2004). In the context of a graph G with n nodes

and m edges, modularity is computed in the following

manner:

Q =

i j



i j

−

× d



δ(C

) (1)

where A is the corresponding adjacency matrix, d

)

denotes the degree of node i( j), C

) is the com-

munity to which node i( j) belongs to. δ(C

) = 1,

if C

= C

, otherwise, 0. A high modularity indi-

cates that there is a dense concentration of connec-

tions within nodes of the same community, while con-

nections between nodes from different communities

are sparse (Fortunato, 2010).

3 PROPOSED BSODCS

ALGORITHM

BSO, inspired by the cooperative behavior of bees,

is a search process that uses a population of artiﬁcial

bees to solve optimization problems. It begins with a

bee called BeeInit, which generates an initial solution

as the reference one (RefSolultion). Then, additional

solutions are generated from RefSolultion, using a

BSODCS: Bee Swarm Optimization for Detecting Community Structure

423

ﬂipping strategy to form the search space. Each so-

lution is assigned to a bee, serving as a starting point

for exploring its neighborhood. After producing their

respective solutions, the bees communicate and share

their best solution through the Dance table.

In order to maintain a balance between exploita-

tion and exploration, BSO uses intensiﬁcation and

diversiﬁcation mechanisms. Intensiﬁcation improves

the best global solution by selecting from the dance

table, while diversiﬁcation explores new areas. The

choice is based on progress, and the selected solution

becomes the new RefSolultion for the next iteration.

Algorithm 1: BSO for detecting community structure.

Data: A network G = (V,E)

Result: Community structure of the network C = {C

,...,C

}

Initialize the algorithm parameters: N (number of bees), itermax

(maximum number of iterations), f lip (search space creation

parameter), and limit (abandonment criterion);

// Initial reference solution, see subsection 3.2;

Re f Solution ← GenerateInitialSolution() ;

Set TabuList = newlist();

Set iter = 0;

while iter < itermax do

// Save RefSolutio in Tabu list;

TabuList ← TabuList + Re f Solutio;

// Determine search space, see subsection 3.3;

for i ← 1 to N do

ApplyFlippingStrategies;

end

Set nbChances = limit;

// Neighborhood exploration (N), see subsection 3.4;

for i ← 1 to N do

NeighborBee ← GenerateNeighborBee(Bee[i]);

// Save best solution in Dance table;

DanceTable ← DanceTable + BestSol(Bee[i], NeighborEBee)

end

// Select the new RefSolution , see subsection 3.5;

BestModularity(DanceTable) > BestModularity(TabuList)

then

Re f Solution ← BestModularity(DanceTable);

nbChances ← limit;

else

if nbChances > 0 then

nbChances ← nbChances − 1;

// Intensiﬁcation;

Re f Solution ← Re f Solution;

else

// Diversiﬁcation

Re f Solution ← GenerateInitialSolution();

end

iter ← iter + 1;

end

BestModularity ← BestModularity(TabuList) ;

Decode the optimal solution to obtain the communities of

network G, C = {C

,...,C

}

To prevent repetition, the latter is stored in a taboo

list. The algorithm continues until an optimal solution

is found or the maximum of iterations is reached.

In this paper, we adapt the BSO algorithm for de-

tecting community structure in networks, which in-

volves speciﬁc considerations. The process is given in

Algorithm 1, and in what follows, we outline the en-

coding of solutions and the evaluation of their quality,

the generation of the initial solution and the determi-

nation of the search region, the local search conducted

by the bees and the selection of the reference solution.

3.1 Solution Encoding

In order to ﬁt the characteristics of networks, we em-

ploy the locus-based adjacency representation (Shi

et al., 2009) to encode solutions representing commu-

nity structures. This encoding scheme offers a signif-

icant advantage by automatically detecting the num-

ber of communities. For a particular network with

n nodes, every individual g in the population is rep-

resented as ⟨g

,...,g

⟩ with n genes, and each g

can take the allele value j in the range of ⟨1, 2, ...,n⟩.

Assigning a value j to the i

gene implies an edge

between nodes i and j in V , resulting in the nodes

i and j belonging to the same community in the de-

tected structure. To extract the community structure

from this representation, a decoding step is required

to identify all connected components of the graph,

ensuring that nodes within the same component are

assigned to the same community. It has been demon-

strated that this decoding method is highly effective

for community detection and can be performed efﬁ-

ciently in linear time (Cormen et al., 2001). For il-

lustration, Fig. 1 shows a network, its corresponding

solution using the locus-based representation, and the

ﬁnal community structure result.

3.2 Initial Reference Solution

Initially, the algorithm generates a solution to repre-

sent the BeeInit’s food source. This solution is gener-

ated randomly or via a heuristic. For community de-

tection problem, a randomly generated solution may

not be feasible. Indeed, it could contain a value j in

the i

position, but no edge (i, j) exists in the net-

work. Therefore, in order to obtain a solution with

certain quality, for each node i, a value j in the i

po-

sition is randomly chosen among its neighbor nodes.

This means that the edge (i, j) exists in the network.

This strategy provides a good starting point for the al-

gorithm and improves the convergence of the method.

WEBIST 2023 - 19th International Conference on Web Information Systems and Technologies

424

Figure 1: Example of a solution representation (Dakiche

et al., 2022).

3.3 Search Space

The search space consists of a collection of N solu-

tions, where N corresponds to the number of bees in

the swarm, since each solution will be assigned to one

bee as a starting point of its local search. These solu-

tions within the search space are generated by ﬂipping

a number of bits equal to n/ﬂip from the reference so-

lution (Refsolution), ﬂip being an empirical param-

eter that signiﬁcantly affects the search process. A

small Flip value implies a local optimum for Refsolu-

tion in the exploitation region, limiting potential im-

provement. Conversely, a high Flip value may cause

the swarm to move away from Refsolution’s region,

potentially overlooking valuable solutions.

To ensure diverse solutions within the search

space, we employ two strategies (Sadeg et al., 2015).

In the ﬁrst strategy, the k

solution is generated by

ﬂipping variables in Refsolution with a separation of

ﬂip bits, starting from the k

position. While in the

second one, the k

solution is obtained by ﬂipping

n/ﬂip contiguous bits, starting from the k

position.

If we consider the example of Fig.1 in which

N = 9 and we take f lip = 3. With the positions la-

beled from 1 to 9, the solutions we obtain by using

the ﬁrst strategy are generated by ﬂipping the follow-

ing positions: (1,4,7), (2,5,8), and (3,6,9), while using

the second strategy produces the solutions generated

by ﬂipping the following positions: (1,2,3), (4,5,6),

and (7,8,9) as illustrated in Fig.2. The positions given

by both strategies are changed by randomly selecting

a neighbor of the corresponding node from its list of

neighbors.

Figure 2: (left) solutions generated by the ﬁrst strategy,

(right) solutions generated by the second strategy.

If the number of generated solutions is insufﬁcient

(less than the deﬁned number of bees), a random ap-

proach can be used. These strategies aim to maintain

distinct solutions while exploring the search space ef-

fectively.

3.4 Neighborhood Procedure

The bees explore their neighborhood for new even-

tually better solutions. To obtain a neighbor solu-

tion, we propose to take advantage of the prior knowl-

edge inferred from the network structure, and use a

Pearson’s-based neighbor procedure. It modiﬁes var-

ious entries of the solution vector using the roulette

method. This method determines the probability of

selecting a pair (i, j) as a component of the new so-

lution. Speciﬁcally, the value j is chosen as the

new value for the input index i with a probability of

p = n

i j

∑

k∈v(i)

, where n

i j

represents the Pearson

correlation between nodes i and j, and v(i) denotes

the set of neighboring nodes of i. Fig. 3 illustrates the

generation of neighboring solutions.

The Pearson’s correlation similarity measure (For-

tunato, 2010) is based on the fact that the nodes be-

longing to the same community are similar to each

other. The Pearson correlation C(i, j) between nodes

and v

is deﬁned as follows:

C(i, j) =

∑

vl∈V

− µ

)(A

− µ

)

nσ

(2)

where A

is the l

element of the i

row in the adja-

cency matrix, µ

∑

/n is the average, and σ

∑

− µ

)

/n is the standard deviation. C(i, j)

takes values between −1 and 1. A value close to 1

means that nodes v

and v

are very similar in a struc-

tural perspective. Otherwise, C(i, j) would be close to

−1. As the Pearson correlation can have negative val-

ues, it cannot be directly used in BSODCS algorithm.

To address this, we apply the logistic function to the

BSODCS: Bee Swarm Optimization for Detecting Community Structure

425

Figure 3: Pearson’s-based neighbor procedure (Dakiche et al., 2022).

aforementioned Pearson correlation, resulting in pos-

itive outputs. These outputs are incorporated into the

algorithm as heuristic information:

i j

1 + e

−C(i, j)

(3)

The more similar nodes v

and v

are the larger value

i j

would take, and the more probably edge (i, j) is to

be taken as a solution component.

3.5 Selection of Reference Solution

The selection of the reference solution, for next itera-

tion, initially relies on the modularity of solutions in

the dance table. However, if the swarm observes a

lack of progress in terms of modularity over a certain

period of time, it incorporates a restart strategy. This

restart enables the swarm to escape from a potentially

stagnant region and explore alternative regions in the

search space. By combining both quality and diver-

sity considerations, the swarm ensures a more com-

prehensive and effective search process.

4 EXPERIMENTAL RESULTS

In this section, our algorithm was tested on a selection

of commonly used networks in the community detec-

tion problem: American college football, Zachary’s

karate club, the Dolphin social network, and Books

about US politics. To assess the quality of the result-

ing community structures, we used modularity as a

quality measure, and compared the results with ﬁve

other swarm based optimization algorithms from lit-

erature: PSO (Chen et al., 2012), ACO (Chen et al.,

2012), BA (Song et al., 2016), ABC (Dakiche et al.,

2022), and BSOCD (Belkhiri et al., 2017). In what

follows, we present the used datasets and discuss the

results.

4.1 Datasets

The American college football network, initially pro-

posed by Girvan and Newman (Girvan and New-

man, 2002), it represents the matches played be-

tween college football teams in the United States dur-

ing the 2000 season. This network consists of 115

nodes representing teams and 616 edges represent-

ing the games played, organized into 12 teams. The

Zachary’s karate club network (Zachary, 1977) de-

scribes the members of a karate club, comprising 34

nodes, and the relationships between them, repre-

sented by 78 edges. Due to internal disagreements

within the club, the members eventually split into two

groups. The Dolphins network (Lusseau et al., 2003),

constructed by Lusseau, focuses on a group of 62 dol-

phins observed over a period of seven years. The net-

work exhibits a division of the dolphins into two dis-

tinct groups, with 159 connections. The Books about

US politics network (Newman, 2006) consists of 105

nodes, representing books on American politics ac-

quired from Amazon.com. The edges between books

denote frequent co-purchasing of books by the same

buyer. The books were categorized into two groups

based on their political alignment (liberal or conser-

vative), with the exception of 13 books that did not

have a clear afﬁliation.

4.2 Results Discussion

The performance of BSODCS, like most metaheuris-

tics, is heavily inﬂuenced by its parameter values. In

our experiments, we determined the optimal param-

eter values through extensive runs using various pa-

rameter combinations. Consequently, we set the pa-

rameters as follows: f lip = 5, limit = 3, the number

of bees N = 20, and the number of iterations 50.

Table 1 provides the modularities obtained from

WEBIST 2023 - 19th International Conference on Web Information Systems and Technologies

426

our algorithm, as well as those from other compara-

tive methods. Our algorithm outperforms the other al-

gorithms for all networks, while ABC algorithm ob-

tains the same results for Karate and Dolphins net-

works. This demonstrates the effectiveness of our

BSODCS in real-world network analysis.

Table 1: Modularity results for all datasets.

Methods Football Karate Dolphins Books

PSO 0.5630 0.3690 - 0.4700

ACO 0.6031 0.4165 0.5628 0.5262

BA 0.5960 0.3920 - 0.4790

ABC 0.6009 0.4198 0.5285 0.5116

BSOCD 0.6040 0.4197 0.5140 -

BSODCS 0.6043 0.4198 0.5285 0,5265

If we consider the Zachary’s karate club, which

naturally consists of two communities of equal size,

our BSODCS algorithm splits the network into four

communities as shown in Fig.4, yielding the highest

modularity value of Q=0.4198 given in Table 1.

Figure 4: Karate Club communities using BSODCS.

5 CONCLUSIONS

In this paper, we investigated the applicability of bee

swarm optimization for community detection prob-

lem. The proposed algorithm, BSODCS, uses the

modularity Q as objective function and starts with

an initial reference solution. A search space is cre-

ated from this reference solution, then a group of bees

collaboratively works to maximize the global func-

tion Q. Each bee operates independently within its

neighborhood and communicates its ﬁndings through

a dance. To assess the effectiveness of our algo-

rithm, we conducted experiments on four real-world

networks. The results obtained demonstrate the valid-

ity and efﬁciency of our method for community de-

tection problem. In future work, we aim to extend

our approach to address community detection prob-

lem in dynamic networks, aiming to further enhance

the quality of the obtained results as well as tracking

communities’ evolution.

REFERENCES

Bedi, P. and Sharma, C. (2016). Community detection in so-

cial networks. Wiley Interdisciplinary Reviews: Data

Mining and Knowledge Discovery, 6(3):115–135.

Belkhiri, Y., Kamel, N., Drias, H., and Yahiaoui, S. (2017).

Bee swarm optimization for community detection in

complex network. In Recent Advances in Information

Systems and Technologies: Volume 2 5, pages 73–85.

Springer.

Brandes, U., Delling, D., Gaertler, M., Gorke, R., Hoefer,

M., Nikoloski, Z., and Wagner, D. (2007). On modu-

larity clustering. IEEE transactions on knowledge and

data engineering, 20(2):172–188.

Cai, Q., Gong, M., Ma, L., Ruan, S., Yuan, F., and Jiao, L.

(2015). Greedy discrete particle swarm optimization

for large-scale social network clustering. Information

Sciences, 316:503–516.

Cai, Q., Gong, M., Shen, B., Ma, L., and Jiao, L. (2014).

Discrete particle swarm optimization for identifying

community structures in signed social networks. Neu-

ral Networks, 58:4–13.

Chen, B., Chen, L., and Chen, Y. (2012). Detecting com-

munity structure in networks based on ant colony op-

timization. In Proceedings of the International Con-

ference on Information and Knowledge Engineering

(IKE), page 1. The Steering Committee of The World

Congress in Computer Science, Computer . . . .

Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C.

(2001). Introduction to algorithms second edition.

Dakiche, N., Benatchba, K., Tayeb, F. B.-S., Slimani,

Y., and Brahmi, M. A. (2022). A hybrid arti-

ﬁcial bee colony algorithm with simulated anneal-

ing for enhanced community detection in social net-

works. In 2022 IEEE/ACM International Conference

on Advances in Social Networks Analysis and Mining

(ASONAM), pages 104–108. IEEE.

Djeffal, M. and Drias, H. (2013). Multilevel bee swarm

optimization for large satisﬁability problem instances.

In Yin, H., Tang, K., Gao, Y., Klawonn, F., Lee, M.,

Weise, T., Li, B., and Yao, X., editors, Intelligent Data

Engineering and Automated Learning – IDEAL 2013,

pages 594–602, Berlin, Heidelberg. Springer Berlin

Heidelberg.

Djenouri, Y., Drias, H., and Chemchem, A. (2013). A

hybrid bees swarm optimization and tabu search al-

gorithm for association rule mining. In 2013 World

Congress on Nature and Biologically Inspired Com-

puting, pages 120–125. IEEE.

Drias, H., Sadeg, S., and Yahi, S. (2005). Cooperative bees

swarm for solving the maximum weighted satisﬁabil-

ity problem. In International Work-Conference on Ar-

tiﬁcial Neural Networks, pages 318–325. Springer.

Fortunato, S. (2010). Community detection in graphs.

Physics reports, 486(3-5):75–174.

BSODCS: Bee Swarm Optimization for Detecting Community Structure

427

Fortunato, S. and Barth

elemy, M. (2007). Resolution limit

in community detection. Proceedings of the National

Academy of Sciences, 104(1):36–41.

Girvan, M. and Newman, M. E. (2002). Community struc-

ture in social and biological networks. Proceedings of

the national academy of sciences, 99(12):7821–7826.

Hafez, A. I., Zawbaa, H. M., Hassanien, A. E., and Fahmy,

A. A. (2014). Networks community detection us-

ing artiﬁcial bee colony swarm optimization. In Pro-

ceedings of the ﬁfth international conference on in-

novations in bio-inspired computing and applications

IBICA 2014, pages 229–239. Springer.

Hassan, E. A., Hafez, A. I., Hassanien, A. E., and Fahmy,

A. A. (2015). A discrete bat algorithm for the com-

munity detection problem. In Hybrid Artiﬁcial Intel-

ligent Systems: 10th International Conference, HAIS

2015, Bilbao, Spain, June 22-24, 2015, Proceedings

10, pages 188–199. Springer.

He, D., Liu, J., Liu, D., Jin, D., and Jia, Z. (2011). Ant

colony optimization for community detection in large-

scale complex networks. In 2011 Seventh Interna-

tional Conference on Natural Computation, volume 2,

pages 1151–1155. IEEE.

Jaradat, A. S. et al. (2018). Community structure detection

using ﬁreﬂy algorithm. International Journal of Ap-

plied Metaheuristic Computing (IJAMC), 9(4):52–70.

Karaboga, D. and Akay, B. (2009). A survey: algorithms

simulating bee swarm intelligence. Artiﬁcial intelli-

gence review, 31:61–85.

Lusseau, D., Schneider, K., Boisseau, O. J., Haase, P.,

Slooten, E., and Dawson, S. M. (2003). The bot-

tlenose dolphin community of doubtful sound features

a large proportion of long-lasting associations: can ge-

ographic isolation explain this unique trait? Behav-

ioral Ecology and Sociobiology, 54:396–405.

Nayyar, A., Le, D.-N., and Nguyen, N. G. (2018). Advances

in swarm intelligence for optimizing problems in com-

puter science. CRC press.

Newman, M. E. (2006). Modularity and community struc-

ture in networks. Proceedings of the national academy

of sciences, 103(23):8577–8582.

Newman, M. E. and Girvan, M. (2004). Finding and eval-

uating community structure in networks. Physical re-

view E, 69(2):026113.

Sadeg, S. and Drias, H. (2007). A selective approach to par-

allelise bees swarm optimisation metaheuristic: Ap-

plication to max-w-sat. Int. J. Innov. Comput. Appl.,

1(2):146–158.

Sadeg, S., Hamdad, L., Benatchba, K., and Habbas, Z.

(2015). Bso-fs: Bee swarm optimization for feature

selection in classiﬁcation. In Rojas, I., Joya, G., and

Catala, A., editors, Advances in Computational Intel-

ligence, pages 387–399, Cham. Springer International

Publishing.

Shi, C., Wang, Y., Wu, B., and Zhong, C. (2009). A new ge-

netic algorithm for community detection. In Zhou, J.,

editor, Complex Sciences, pages 1298–1309, Berlin,

Heidelberg. Springer Berlin Heidelberg.

Song, A., Li, M., Ding, X., Cao, W., and Pu, K. (2016).

Community detection using discrete bat algorithm.

IAENG International Journal of Computer Science,

43(1):37–43.

Yang, J., McAuley, J., and Leskovec, J. (2013). Community

detection in networks with node attributes. In 2013

IEEE 13th international conference on data mining,

pages 1151–1156. IEEE.

Zachary, W. W. (1977). An information ﬂow model for con-

ﬂict and ﬁssion in small groups. Journal of anthropo-

logical research, 33(4):452–473.

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