=Paper=
{{Paper
|id=Vol-2215/paper9
|storemode=property
|title=Recommending Items in Social Networks using Cliques-Based Trust
|pdfUrl=https://ceur-ws.org/Vol-2215/paper_9.pdf
|volume=Vol-2215
|authors=Lidia Fotia
|dblpUrl=https://dblp.org/rec/conf/woa/Fotia18
}}
==Recommending Items in Social Networks using Cliques-Based Trust==
https://ceur-ws.org/Vol-2215/paper_9.pdf
Recommending Items in Social Networks using
Cliques-Based Trust
Lidia Fotia†
†
DIIES, University Mediterranea of Reggio Calabria, Via Graziella, Località Feo di Vito, 89122 Reggio Calabria,
Italy, lidia.fotia@unirc.it
Abstract—Thematic groups are gaining a lot of attention and evaluating the level of trustworthiness of an interlocutor.
high centrality in online community, as users share opinions Commonly, in the traditional OSN contexts, the reputation of
and/or mutually collaborate for reaching their targets. In this a user is evaluated by averaging feedbacks provided by all the
paper we consider the concept of clique in the social networks.
A clique is a group of actors connected to each other more closely other users belonging to the same community.
than the overall network of which they are a part. In the common In the past literature, there are many approaches based on
language, the term clique means an informal and restricted global reputation [4]–[6] which is calculated on the evaluation
social group formed by people who share common interests or of the users’ behaviours shared with the entire community,
characteristics. This paper proposes a new trust measure in social and local reputation [7] that is based on the recommendations
networks which focuses on cliques. In particular, we represent
this scenario by means of a specific model, and we introduce coming by the entourage of the user (friends, friends of friends
an algorithm for detecting trust recommendations. We show a and so on). The first type of approaches shows a limitation
complete example of how our approach works. due to the difficulty of taking into account the effects of
Index Terms—Recommendation, Online Communities, Trust, malicious or fraudulent behaviours, thus making the feedback
Group. themselves. Also, they are limited by the fact they need
a training phase in generating recommendations. The latter
I. I NTRODUCTION overcome these limitations but they do not consider a group-
based structure [8]–[10].
In the last few years, the number of users of online social In this paper we present an approach to find a certain class
networks has grown at an unprecedented rate. Many social of groups of users linked by trust relationships. In particular,
networks provide tools which recommend friends, and some- we apply the BronKerbosch algorithm [11] to find the cliques
times resources, to their users. These tools rely on a notion in a social network. The algorithm is a simple backtracking
of similarity between users or between a user and a resource. procedure that recursively solves subproblems specified by
Obviously, they are not able to recommend to a user new social three sets of vertices: the vertices that are required to be
networks potentially relevant to him. included in a partial clique, the vertices that are to be excluded
For this reason, an important target in Online Social Net-
from the clique, and some remaining vertices whose status still
works (OSNs) is to implement recommender systems capable
needs to be determined. Moreover, our approach depends on
to supply users with profitable suggestions about users to
two main parameters: the relevance given to the reliability with
contact as interlocutors or interesting content to access. To
respect to the reputation and the threshold of recommendation
achieve this goal it is necessary to consider the opinions
under which a product can be considered as not interesting. We
provided by the community about the other users or the OSN
propose an algorithm for detecting trust recommendations for
content [1]–[3]. However, some users have malicious or even
a user considering the recommendations that come from users
fraudulent behaviours in OSNs, thus the recommender sys-
within his own cliques and those of other cliques weighted
tems could generate unreliable recommendations. Therefore,
with the global reputation. We also present a complete example
in these contexts, it is necessary to introduce the concept of
of how our approach works and an application to a real social
trust.
network.
The issue of trusting interlocutors largely emerged in online The paper is organised as follows. In the next section,
e-Commerce communities as, for instance eBay, and now it is we describe the BronKerbosch algorithm. In Section III, we
discussed in many OSNs which allow their users to create provides technical details about our approach for finding trust
and share contents with other users as well as opinions. For recommendations about products. In Section IV, we survey
example, in the social networks EPINIONS1 and CIAO2 the the related work of the recent literature. In Sections V and VI,
users supply reviews about commercial products of different we describe a possible case study of the application. Finally,
categories. Almost all of these platforms tackle this goal by in Section VII we draw our conclusions and illustrate some
adopting a reputation system. possible future works.
Reputation is a form of indirect trust, where a user takes
advantage from the opinions coming from other users for II. T HE B RON K ERBOSCH A LGORITHM
1
www.epinions.com The BronKerbosch algorithm [11] is a recursive backtrack-
2
www.ciao.it ing algorithm used to find all maximal cliques in a graph. A
51
recursive call to the BronKerbosch algorithm supplies three able to evaluate y’s trustworthiness. In order to compute the
sets of vertices C, S, and B as arguments, where C is a reputation, we adopt the notion of
(possibly non-maximal) clique and S ∪ B = Γ(C) are the
vertices that are adjacent to every vertex in C. Within the 1 X
REPy = hρ (1)
recursive call, the algorithm lists all cliques in S ∪ C that are hmax |REVy |
ρ∈REVy
maximal within the subgraph induced by S ∪ C ∪ B.
where |REVy | is the set of the reviews made by the user y
The algorithm selects v ∈ S to add to the clique C, and
and h is the helpfulness, i.e., it is associated with each review
makes a recursive call in which v has been moved from C to
and represents the level of satisfaction of the other users for
S. In this phase, it restricts B to the neighbors of v because
that review. To normalise REPy , we divide it by the maximum
non-neighbours cannot affect the maximality of the resulting
value of the helpfulness hmax . REPy assumes values ranging
cliques. At the end of the recursive call, v is moved to B. The
in the interval [0 . . . 1]R. Finally, we define T RU STx,y of x
recursion procedure ends when S and B are empty and the
about y in the interval [0 . . . 1] as follows:
output C is a maximal clique. To obtain all maximal cliques
in the graph, This recursive algorithm is called with S equal
T RU STx,y = α · RELx,y + (1 − α) · REPy (2)
to the set of all vertices in the graph and with C and B empty.
The algorithm is shown in Listing 1. where α is a real number, ranging in [0...1], which is set
by x to weight the relevance he/she assigns to the reliability
Listing 1. BronKerbosch algorithm with respect to the reputation.
p r o c B r o n K e r b o s c h ( C , S , B)
1: i f (S ∪ B = 0) then
2: r e p o r t C a s a maximal c l i q u e A. The Trust-Based Recommendation System without and with
3 : end i f cliques
4 : f o r e a c h v e r t e x v ∈ S do
5: B r o n K e r b o s c h ( S ∩ Γ(v) , C ∪ {v} , B ∩ Γ(v) ) At this step, x receives some recommendations about the
6: S := S\{v} community products. In particular, RECxp is the recommenda-
7: B := B ∪ {v} tion that the user x receives about the product p. It is calculated
8 : end f o r as follows:
p
P
p y∈A,y6=x T RU STx,y · ratey
RECx = P (3)
y∈A,y6=x T RU STx,y
III. O UR SCENARIO
where ratepy is the review of the the user y about the product
We introduce a virtual community V , formally denoted as p (a number between 1 and 6), weighed by the trust of y.
V = hA, Ci, where A is the set of agents joined with V and C This means that his/her opinion about a product is taken into
is the set of cliques contained in V . Moreover, each clique c is account if his/her trustworthiness is high.
handled by an administrator agent ac . All such communities 1) Cliques: Now, we introduce the clique’s concept in the
are organised in social structures based on social relationship community. The cliques are calculated following the BronKer-
(like, Facebook or Twitter). The formation of a group (i.e. bosch algorithm described in the section II. In this case, we
cliques) is a process based on two main events: a user asks suppose that the trust perceived by an agent x with respect
for joining with a group and the administrator of the group to the component of its clique is equal to tx,y + ∆, instead
accepts or refuses the request. the agent x considers the trust that user has in the whole
In our proposal, we introduce two measures to ensure that community (see Equation 2). In other words, if a user y
the recommendation system generates correct outputs. The first belongs to the same clique of x, tx,y can be increased by
measure is the trust. We denote it by the mapping T RU STx,y a value ∆. Being part of the same clique, even if x and y do
that receives as input two agents x and y and produces as not know each other directly, they have interests in common
output a value representing the degree of trust between two and there is an indirect connection between them. ∆ is a
agents: T RU STx,y = 0 (resp. T RU STx,y = 1) means that x real number, ranging in [0...1], which is set by x to weight
assigns the minimum (resp. maximum) trustworthiness to y. the relevance he/she assigns to the clique with respect to the
The trust measure is asymmetric. If x does not have a sufficient standard configuration. tx,y + ∆ must not exceed 1.
direct knowledge of y, the agent must use the recommenda-
tions coming from the other agents of the community. For IV. R ELATED W ORK
this reason, we introduce a more general trust measure, by Concerning the concept of trust, there are several proposals
combining two components RELx,y and REPy , where (i) in the literature and in several domains [12]–[16] In particular,
RELx,y is the direct reliability of y because has interacted a large number of papers in the literature investigated on the
in the past with x while (ii) REPy is the global reputation topic we deal with here, therefore, in this section we cite
of y, i.e. the trustworthiness that the whole community has only those approaches which we consider comparable with
in y. In particular,
[ RELx,y assumes values ranging in the that discussed in this paper.
domain [0 . . . 1] {N U LL}, while RELx,y = NULL means Sherchan et al. [17] present an important review of trust,
that y did not have past interactions with x and thus it is not in which they comprehensively examine trust definitions and
52
We apply the BronKerbosch algorithm (see Section II) to the
graph depicted in Figure 1, which also contains the final set of
cliques obtained by the algorithm itself. In our case, there are
four cliques called c1 , c2 , c3 and c4 . Moreover, the values of
REL are as follows: REL1,2 = 0.6, REL1,5 = 1, REL1,7 =
0, 82, REL1,8 = 0, 4, REL1,9 = 0, 3, REL1,11 = 0, 1,
REL2,3 = 0, 81, REL2,4 = 0, 81, REL3,2 = 0, 9, REL3,4 =
0, 85, REL4,2 = 0, 9, REL4,3 = 0, 81, REL5,1 = 0, 9,
REL5,7 = 0, 85, REL5,11 = 0, 4, REL6,8 = 0, 9, REL7,1 =
0, 81, REL7,5 = 0, 95, REL8,6 = 0, 81, REL9,10 = 0, 86,
REL9,11 = 0, 85, REL10,9 = 0, 91, REL10,11 = 0, 85,
REL11,9 = 0, 86, REL11,7 = 0, 3 and REL11,10 = 0, 9.
In particular, in our example, there are nine products that are
divided in three main categories called Electronics, Informatics
Fig. 1. The cliques obtained by applying the BronKerbosch algorithm. and Software, these are shown in Table I, while in Table II,
we show an example of dataset.
measurements, from multiple fields including sociology, psy- productID name categoryID
chology, and computer science. Trust models [18]–[21] allow 1 Car TomTom, Display 5” Electronics
2 Smartphone Android 5.1 Electronics
to exploit information derived by direct experiences and/or 3 TV HD Ready 15,6” Format 16:9 Electronics
opinions of others to trust potential partners by means of a 4 Notebook 15” i7, RAM 8 GB, HDD 500GB Informatics
5 Black and white laser printer Informatics
single measure [22], [23]. Xia et al. [24] build a subjective trust 6 Tablet 7”, Wi-Fi, 8 GB Informatics
management model AFStrust, which considers multiple factors 7 Microsoft Windows 7 PRO SP1 32/64-bit Software
8 Microsoft Office 365 Personal - 32/64 Bit Software
including direct trust, recommendation trust, incentive function 9 Nuance Power PDF Standard Software
and active degree, and treats those factors based on the analytic
TABLE I
hierarchy process (AHP) theory and the fuzzy logic rule. L IST OF PRODUCTS
[25] describes how to build robust reputation systems using
machine learning techniques, and defines a framework for
translating a trust modelling problem into a learning problem. In our model, we have associated with each agent a profile
In many disciplines, there is a population of people which contained, as unique feature, the reputation to review the
should be optimally divided into multiple groups based on products. This reputation has been computed by averaging, on
certain attributes to collaboratively perform a particular task all the reviews posted by the agent, the helpfulness associated
[26], [27]. The problem becomes more complex when some with each review, where the helpfulness is an information
other requirements are also added: homogeneity, heterogene- available on the dataset and obtained by the opinions
ity or a mixture of teams, amount of consideration to the expressed by the users of the community. We obtain that the
preferences of individuals, variability or invariability of group reputation values (see Equation 1) of the agents belonging
size, having moderators, aggregation or distribution of persons, to our scenario are as follows: REP1 =0.79; REP2 =0.76;
overlapping level of teams, and so forth [5], [28]–[30]. Basu REP3 =0.66; REP4 =0.42; REP5 =0.96; REP6 =0.62;
et al. [31] consider the problem of how to form groups such REP7 =0.66; REP8 =0.5; REP9 =0.77; REP10 =0 and
that the users in the formed groups are most satisfied with REP11 =0.58. At this point, we calculate the trust (see
the suggested top-k recommendations. They assume that the Formula 2). Fixed the agent a1 , we compute the opinion
recommendations will be generated according to one of the (i.e., trust) that a1 has with regard to other agents. Recall
two group recommendation semantics, called Least Misery and that this value changes with α. We consider three values of
Aggregate Voting. Rather than assuming groups are given, or α. In particular, α=1 means that the agent a1 considers only
rely on ad hoc group formation dynamics, their framework the opinions of the agents with whom he/she interacted in
allows a strategic approach for forming groups of users in the past (contrariwise, α=0). Finally, α=0.5 means that the
order to maximise satisfaction. In [32], the authors reveal how agent a1 considers in the same way both the opinions of the
these problems can be mathematically formulated through a agents with whom he/she interacted both others. For detail,
binary integer programming approach to construct an effective see Table IV. Let ξ be a threshold fixed by the agent a1 , we
model which is solvable by exact methods in an acceptable suggest only those products that have RECap greater than ξ
time. (in our case, we fix ξ > 4). In particular, we note that the
agent a5 that has a high value of reliability for the agent a1
buys the products p8 and p9 . Also, a5 assigns to them a high
V. A N E -C OMMERCE CASE STUDY
rate while the rest of the community gives a very low rate.
Now, we explain how it is possible to use cliques to generate Surely a1 would be very interested in these products, because
the recommendations of products for the users inserted into an he/she trusts a5 with a high value. At this point, we see how
online e-Commerce communities. As an example, we propose the algorithm behaves. The agent a1 receives, at the current
to model our community by a graph G. step, some recommendations by the other agents, in response
53
userID productID categoryID rating helpfulness u v tuv (α = 0) tuv (α = 0.5) tuv (α = 1)
1 9 3 3 5 1 2 0.76 0.68 0.6
1 5 2 3 5 1 3 0.66 0.33 0
1 6 2 5 2 1 4 0.42 0.21 0
1 7 3 1 6 1 5 0.96 0.98 1
1 8 3 5 6 1 6 0.62 0.31 0
2 1 1 3 5 1 7 0.66 0.74 0.82
2 2 1 4 6 1 8 0.50 0.45 0.4
2 5 2 4 5 1 9 0.77 0.54 0.3
2 6 2 5 5 1 10 0 0 0
2 8 3 5 2 1 11 0.58 0.34 0.1
3 1 1 4 2
3 8 3 5 3 TABLE IV
3 2 2 3 5 S IMULATION PARAMETERS WHEN VARYING α
3 4 2 6 6
4 1 1 5 1
4 3 1 5 2
4 6 2 3 6
4 9 3 2 1 can consider the assumption made in the Section III. Recall
5 1 1 2 6
5 3 1 2 6 that, for the agents that are in the same cliques, the trust is
5 4 2 4 5 equal to tx,y + ∆. If tx,y + ∆ is greater than 1, tx,y = 1. This
5 8 3 6 6
5 9 3 6 6 means that for any value of Delta, tx,y can not assume a value
6 6 2 2 6 greater than 1. Now, we can calculate the recommendations
6 5 2 4 2
6 7 3 1 4 (see Equation 3) to the agent a1 for all the products in the
6 8 3 0 3 community in presence of the cliques and ∆ = 0, 5. The table
7 1 1 4 4
7 9 3 4 6 V shows the results obtained.
7 5 2 5 3
7 8 3 4 3 α p1 p2 p3 p4 p5 p6 p7 p8 p9
8 1 1 5 2 0 3.74 3.76 3.33 4.79 4.42 3.64 1.00 3.65 3.99
8 3 1 5 0 0.5 3.92 3.83 3.16 4.47 4.50 3.96 1.00 3.90 4.17
8 6 2 2 5 1 3.32 4.00 3.03 4.00 4.62 4.52 0 4.37 4.49
8 9 3 3 5
9 2 1 4 4
9 6 2 2 5 TABLE V
9 9 3 3 5 T HE RECOMMENDATIONS TO THE AGENT a1 IN THE PRESENCE OF
11 1 1 5 3 CLIQUES
11 3 1 3 3
11 2 2 4 3
11 9 3 4 5
The results in the presence of the cliques are best, because
TABLE II a3 and a7 know better a1 and consequently are able to make
A N EXAMPLE OF DATABASE targeted recommendations.
VI. T HE APPLICATION OF OUR PROTOCOL TO THE SOCIAL
to previous recommendation requests (see Table III). If α=1, NETWORK CIAO
we suggest to a1 the products p5 , p6 , p8 and p9 . In this case, In this section, we describe the implementation of our
we consider the recommendations that come from agents that protocol for the social network CIAO. CIAO dataset, described
have a high reliability. In fact, these products were acquired in [33], consists in a matrix with a total of about 36k rows,
and evaluated good by agents a5 and a2 . Comparing these each of them representing an event in the virtual community,
results with truly user-purchased products, it is visible that in the form userID, productID, categoryID, rating, helpful-
four out of four products were actually purchased by a1 . If ness, timestamp. More in detail, CategoryID represents the
α=0, we suggest to a1 the products p4 and p5 . This is correct commercial category of the product for which the user has
because they are products purchased by agents who have a released a rating, and the helpfulness (a number between 1 and
high reputation in the community. But, these agents did not 6) represents the level of satisfaction of the other users for that
interact directly with a1 therefore they do not know his/her rating. In addition, a dataset representing trust relationships is
preferences. Indeed, only the product p5 is of interest to a1 . available. It consists in a list of pairs of user IDs (x, y), where
If α=0.5, we suggest to a1 the products p4 , p5 and p9 . This each of them represents a trust relationship among user x and
choice is a good compromise, since two of the three products user y.
are of liking for the agent a1 . The measure REP (see Formula 1) for each agent is
calculated using the code shown in Algorithm 1.
α p1 p2 p3 p4 p5 p6 p7 p8 p9
0 3.74 3.76 3.35 4.82 4.32 3.62 1.00 3.61 3.95
0.5 3.56 3.83 3.17 4.50 4.42 3.95 1.00 3.89 4.17 Listing 2. Algorithm 1: computeREP
1 3.28 4.00 2.87 4.00 4.58 4.52 0 4.42 4.49 Input r e v : t h e r e v i e w m a t r i x g e n e r a t e d by t h e a g e n t s
Input numAg : t h e number o f a g e n t s i n t h e community
Variable j : a r e a l number
TABLE III Variable x : a r e a l number
T HE RECOMMENDATIONS TO THE AGENT a1 Variable c o n t S c o r e : a r e a l number
Variable sum : a r e a l number
Variable r e p V a l u e : a v e c t o r
1 : sum : = 0
With the introduction of the cliques in the community, we 2: contScore :=0
54
3 : for x : = 1 to numAg do T RU STi,m = α + (1 − α) · repV alue[m] (Line 3). If there
4: for j : = 0 to length of r e v do
5: if x = r e v [ j ] [ 1 ] then
is no interaction between i and m (Line 5), the algorithm
6: contScore := contScore + 1 calculates T RU STi,m = (1 − α) · repV alue[m] (Line 6).
7: sum : = sum + r e v [ j ] [ 4 ] ;
8: end if
If there is a direct link between i and m but they have at
9: end for least a clique in common (Line 8), the algorithm calculates
1 0 : if ( sum 6= 0 ) AND ( c o n t S c o r e 6= 0 ) then
11: r e p V a l u e [ x ] : = ( sum / c o n t S c o r e ) / 6 ;
T RU STi,m = α + (1 − α) · repV alue[m] + delta and store
11: sum = 0 ; it in the variable verif y (Line 9). The algorithm checks the
12: contScore =0;
1 3 : end if
trust to verify if it takes a value equal to or less than 1 (Lines
1 4 : else 10-14). Finally, if there is no direct link between i and m but
15: repValue [ x ]=0;
1 6 : end else
they have at least a clique in common (Line 17), the algorithm
1 7 : end for calculates T RU STi,m = (1 − α) · repV alue[m] + delta and
First, for each agent x of the community (Line 3), if the verify if its value is equal to or less than 1 (Lines 18-23).
index x corresponds to the one contained in the review matrix Whenever T RU STi,m 6= 0, its value is inserted into an output
(Line 3), the algorithm saves all the helpfulness related to its file (Lines 26-27).
reviews within the variable sum (Line 7) and increases the Finally, the measure RECxp (see Formula 3) for each agent
variable contScore to keep track of the number of reviews x is calculated using the code shown in Algorithm 3.
affected by x (Line 6). At this point, if x has issued at least Listing 4. Algorithm 3: computeREC
one review (Line 10), the algorithm saves to the x position of Input r e v : t h e r e v i e w m a t r i x g e n e r a t e d by t h e a g e n t s
the vector repV alue the value of REP (Line 11). Otherwise, Input t r u s t : t h e t r u s t m a t r i x o f t h e a g e n t s
Input numProd : t h e number o f p r o d u c t s i n t h e community
the rep value is set to zero (Line 15). Variable r e c P r o d : t h e m a t r i x o f recommended p r o d u c t s
The measure T RU ST (see Formula 2) for each agent is Variable recAg : a r e a l number
Variable s : a r e a l number
calculated using the code shown in Algorithm 2. Variable sumRec : a r e a l number
Variable y : a r e a l number
Listing 3. Algorithm 2: computeTRUST 1 : recAg : = 1
Input a l p h a : a r e a l number 2: s :=0
Input d e l t a : a r e a l number 3 : sumRec : = 0
Input i : a r e a l number 4 : for y : = 1 to numProd do
Input m: a r e a l number 5 : for n : = 0 to length of r e v do
Input c l i q u e s : an a r r a y L i s t o f a r r a y L i s t 6: if ( y = r e v [ n ] [ 1 ] ) AND ( recAg 6= r e v [ n ] [ 0 ] )
Input r e p V a l u e : a v e c t o r AND ( t r u s t . CONTROL( recAg , r e v [ n ] [ 0 ] ) = t r u e ) then
Input a d j a c e n c y m a t r i x : a S p a r s e M a t r i x 7: s : = s + r e v [ n ] [ 3 ] ∗ t r u s t ( recAg , r e v [ n ] [ 0 ] )
Input t r u s t o u t f i l e : a f i l e 8: sumRep : = sumRep + t r u s t ( recAg , r e v [ n ] [ 0 ] )
Variable i n t e r : a H a s h S e t 9: end if
Variable v e r i f y : a r e a l number 1 0 : end for
Variable d e l t a : a r e a l number 1 1 : if ( s 6= 0 ) AND ( sumRec 6= 0 ) then
1: i n t e r : = INTESECT ( c l i q u e s ( i ) , c l i q u e s (m) ) 1 2 : r e c P r o d ( recAg , y ) : = s / sumRec
2 : if ( a d j a c e n c y m a t r i x . CONTROL( i , m) = t r u e ) AND ( lenght 1 3 : end if
of i n t e r = 0 ) then 1 4 : else
3: t r u s t ( i , m) : = a l p h a + (1− a l p h a ) ∗ r e p V a l u e [m] 1 5 : r e c P r o d ( recAg , y ) : = 0
4 : end if 1 6 : end else
5 : else if ( a d j a c e n c y m a t r i x . CONTROL( i , m) = f a l s e ) AND ( lenght 17: s := 0
of i n t e r = 0 ) then 1 8 : sumRec : = 0
6: t r u s t ( i , m) : = (1− a l p h a ) ∗ r e p V a l u e [m] 1 9 : recAg : = recAg + 1
7 : end else if 1 7 : end for
8 : else if ( a d j a c e n c y m a t r i x . CONTROL( i , m) = t r u e ) AND ( length
of i n t e r 6= 0 ) then First of all, the algorithm initialises the variables recAg, s
9: v e r i f y : = a l p h a + ((1 − a l p h a )∗ r e p V a l u e [m] ) + d e l t a
10: if ( v e r i f y <= 1 ) then
and sumRec (Lines 1-3). recAg stores the agent’s index to
11: t r u s t ( i ,m) : = v e r i f y which we want to recommend the product. It is incremented at
12: end if
13: else
the end of each for loop (Line 19). For each product y of the
14: t r u s t ( i ,m) : = 1 community and for each row of rev (Lines 4-5), if there is a
15: end else
1 6 : end else if
revision for the product y that has not been inserted by recAg
1 7 : else if ( a d j a c e n c y m a t r i x . CONTROL( i , m) = f a l s e ) AND ( length and there is a direct link between the reviser (i.e., rev[n][0]
of i n t e r 6= 0 ) then
18: v e r i f y : = ((1 − a l p h a )∗ r e p V a l u e [m] ) + d e l t a ;
) and recAg, the algorithm calculates the numerator and the
19: if v e r i f y <= 1 then denominator of the Formula 3 (Lines 6-8). Then, the algorithm
20: t r u s t ( i ,m) : = v e r i f y
21: end if
verifies that these values are different from zero and stores this
22: else value in a matrix in row recAg and column y (Lines 11-15).
23: t r u s t ( i ,m) : = 1
24: end else
When the for loop on the revision matrix ends, s and sumRec
2 5 : end else if are reset and recAg is increased by 1 (Lines 17-19).
2 6 : if ( t r u s t ( i ,m) >0) AND ( t r u s t o u t f i l e 6= NULL) then
27: i n s e r t t r u s t ( i ,m) i n t r u s t o u t f i l e
2 8 : end if VII. C ONCLUSION
First, the algorithm verifies if the agents i and m have In this paper, we introduce a trust model that integrates
cliques in common and stores them in inter (Line 1). The reliability and reputation in an OSN organised by cliques.
algorithm performs some checks to determine how to calculate In particular, we considered two important parameters: the
the trust. If there is a direct link between i and m but they do relevance given to the reliability with respect to the reputation
not have cliques in common (Line 2), the algorithm calculates and the threshold of recommendation under which a product
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