Temporal Social Network: Group Query Processing∗

Xiaoying Chen1 Chong Zhang2 Yanli Hu3 Bin Ge4 Weidong Xiao5

Science and Technology on Information Systems Engineering LaboratoryNational University of Defense Technology, Changsha 410073, P.R.China

andCollaborative Innovation Center of Geospatial Technology, China

{1chenxiaoying1991, 2leocheung8286}@yahoo.com 3smilelife1979@163.com4gebin1978@gmail.com 5wilsonshaw@vip.sina.com

Abstract—With the development of on-line social networks,more and more users and sellers are interested in group analyticswhich provides insights into common interests with variousrelationships. This paper addresses this problem from temporalaspect, i.e., temporal group query (TGQ) which gives people thehistorical view for group forming and changing. To efficientlyachieve our goal, we propose two structures to index temporalsocial network (TSN), and then a simple naive searching methodis designed to process the TGQ, after that we argue a moreefficient approach can be implemented by update operationsinstead of iterative graph generations, which we call optimizedmethod. We conduct experiments on real-synthetic dataset, andthe results show that our indexes and searching algorithms arecapable, and optimized method is much more efficient than thenaive one.

I. INTRODUCTION

Due to the increasing popularity of social networks and vastamount of information in them, there have been many effortsin enhancing web search based on social data. Social networkscontain data about the network, i.e., data about users and theirsocial relations, data about the activities that users participatein. Besides the graph structure, another important dimensionof social network is dynamic attribute. For instance, loginsor logouts of a user represents changes in the users’ on-linestatus. Also, new content is added through user activities (suchas posting text, photo) representing respective changes in theusers’ interests. This temporal aspect of information in socialnetwork would influence social network query either explicitlyby enabling users to query for particular time points or periods,or implicitly by providing the fresher results, e.g., find someusers who are active during a certain period, or find someactivities posted at some time. Such queries add temporal axisto user requirement, we call it temporal social network query.

In our previous work, we introduced temporal social net-work, and address three query types, namely Friends ofInteresting Activities (FIA) query, Users of Time Filter (UTF)query and Group of Users with Relationship Duration (GURD)query. In GURD query, it aims to find a set of groups, wherethe number of users in each group is equal to a given number,and average intimate degree – which is measured by averagerelationship duration – of it satisfies a given value, and all themembers of it have taken part in some given activities. In this

∗This work is supported by NSF of China grant 61303062 and 61302144.

paper, we argue that GURD is not sufficient for analyzing thechanges of groups, which is an essential module for temporalsocial networks analytics. Thus, we intend to extend GURDquery to a more generalized and applicable one to adapt moretemporal queries in real world. Here, we call it TemporalGroup Query (TGQ).

TGQ is essential, for instance, when the system analystwould like to observe and analyze the formation and changesof groups, historically. For example, they aim to find a setof groups, each group with all member participating in theactivity labeled with ‘presidential election’ during last twoweeks, and average on-line duration is not less than 24 hoursduring last two weeks. The result of this query should beappropriately in the form: {< g1={u1, u2, . . . }, t1, t2>,< . . . >, . . .}, where g1 is a satisfying group valid during[t1, t2].

For efficiently answer TGQ query, we design two indexes,one is called Temporal Activity tree (TA-tree) indexing par-ticipating time and keywords’ activity , the other is TemporalFriendship tree (TF-tree) indexing versions of relationships.We first devise an approach naively iterate each relationshipchanging time point, and construct the satisfying group. How-ever, we argue that the naive method is not efficient, thus wedesign a more efficient algorithm to accelerate the processing,in particular, it is a series update operations to an initial graphsand check which updated graph is satisfied. Due to less timefor constructing connected graph, it is more efficient than thenaive one. In this paper, we make the following contributions:

• We propose a more applicable query type, temporal groupquery, to answer group query in temporal social network.

• We design two approaches to process TGQ, one is naiveiterative, the other is an optimized one.

• We conduct experiments on real-synthetic hybrid dataset,and results show our method is efficient.

The rest of this paper is organized as follows. Relatedworks are surveyed in section 2. Problem is formally definedin section 3. In section 4, two index TA-tree and TF-treeare presented, followed by query processing in section 5. Insection 6, we carry out our experiments. Finally, section 7concludes the paper with directions for future works.

II. RELATED WORKS

Some of the relevant works of temporal social network studyfocus on efficient algorithms and data structure for searchingdata. And some others propose some typical kinds of temporal-social query that can be applied to life application. We haveproposed three kinds of queries, namely FIA, UTF and GURDquery in [1]. GURD query is a kind of temporal group query,which aims to find a set of groups, where the number of usersin each group is equal to a given number, and average intimatedegree of it satisfies a given value, and all the membersof it have taken part in some given activities. We proposetwo index structures, TUR-tree and TUA-tree for acceleratingquery process. Algorithms of query processing for the threequeries are finally proposed.

There are many other works introduce many kinds of groupqueries, such as [2], [3], [4]. Social-Temporal Group Query(STGQ) [2], which considers the available time of candidateattendees and their social relation, aims to find activity timeand attendees with minimum total distance to the initiator.However, in STSG, the time dimension is only considered asavailable time for attendees, which can be dealt with afterSocial-Group Query (SGQ).

In the other hand, adding the spatial dimension into socialnetwork would bring about different group queries. Socio-Spatial Group Query (SSGQ) [3] finds a group of attendeesclose to rally point and ensure that the selected attendees havea good social relationship to create a good atmosphere in theactivity. There are many similar queries, for example, Circle ofFriends (CoF) [4] finds a group of friends whose members areclose to each other both socially and geographically. These twoquery problem are both NP-hard (because social restrictionsdiverse), but without time dimension.

As there are many kinds of temporal social network queries,it is impossible to study all of them. So Kostas Stefanidiset.al.[5] define a logical algebra that provides a set of oper-ators required for temporal social network query evaluation.However, this work only provides a logical algebra withoutany storage model and query processing detail which is theimportant factor to the effectiveness of this framework. As wehave introduced above, there are few previous studies considerthe efficient query processing in temporal social group queryin historical view.

III. PROBLEM DEFINITIONS

Given an undirected graph G=(V , E), V =U∪A. Each vertexui in U represents a user in the community and is associatedwith a time interval [uts, ute), meaning the valid period duringwhich ui exists (or being logon status) in community, and [uts,∗) means ui is still in the community now. For a given socialnetwork graph G, there is also a set A⊂V , in this paper, weuse term activity to denote social event in the social network,e.g., publishing a post, sharing a link and etc. Without lossgenerality, each activity can be represented as < aid,Wa >,where aid is the activity identifier, Wa is a keyword set todescribe the activity.

Each edge (vi, vj) in E has two forms: (ui, uj) and (ui, aj).(ui, uj) represents a friend relationship between user ui anduj , and it is also associated with a time interval [ets, ete), inwhich ets means the time when the relationship is establishedand ete means the time when the relationship is removed.

Each ui in G can connect to an activity ak in A, whichmeans that ui gets involved in ak, formed as (ui, ak). We useterm participation to describe relationship between user andactivity, e.g., in social network, user may post some texts, orforward other’s post, or share a link of web page, or commentother’s activity, or add some activity into favorite, in general,we call these actions as participations.

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Fig. 1. Temporal Social Network Example

Figure 1 illustrates a temporal social network, where usersand activities are plotted as dots and triangles, respectively.The relationship are divided into two categories: user-to-user(solid line) and user-to-activity (dashed line). And the labelon edge indicates time interval of relationship or time stampwhen a user participate in an activity. For instance, user u1

logins community at time ut1 and does not logout at current,and user u1 and u2 become friends at et1 and unfriend eachother at et3, and u4, u7 and u2 participate in a2 at t4, t5 andt6, respectively.

Then we formally give definition of TGQ, a TGQ (W ,[ts, te], tol) aims to find a set of groups, in which, eachgroup is a connected graph, and all members have participatedin the activities with keywords in W during period [ts, te],and the average on-line duration (AOD) (during [ts, te]) ofthe members is not less tol. Here on-line duration (AOD) isdefined as:

AOD =

∑ni=1 onlineduration(ui)

n(1)

where n is the cardinality of the group, onlineduration(ui)calculates on-line duration of user ui.

IV. INDEXES DESIGN AND FUNCTIONS

We believe that for a TGQ (W , [ts, te], tol), two kindsof temporal predicates should be taken into consideration ofbuilding indexes. One is the temporal predicate [ts, te] forparticipation time, and the other is friendship valid periodpredicate for generating groups with valid period. Thus, wedesign two indexes to accelerate query processing. One indexis for finding which users participating in the activities withkeywords in W during [ts, te], and the other one aims to

process the query – given a time period, find pairs of userswho are friends during the period.

The first index we call it Temporal Activity tree (TA-tree),which is actually a B+-tree injected with Bloom Filter[6]. Inparticular, the data item (entry in leaf node) to be indexed isin the form <ui, tp, ak,Wak

>, where ui is a user identifier, tprepresents the time user ui participates in activity ak, and Wak

is the keyword set describing ak. B+-tree is built accordingto the key tp, and the keyword sets of all entries in each leafnode constitute a Bloom Filter BF , and BF serves as filterwith pointers in internal nodes. Figure 2 illustrates an exampleof TA-tree. We use a querying function to represent retrievalfunction of TA-tree, R=TARetrv([ts, te], W ), which meansto find user set R participating in the activities with keywordsin W during [ts, te].

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Fig. 2. TA-Tree Example

The second index is Temporal Friendship tree (TF-tree),which is a kind of MVB-tree[7], indexing the temporal friendrelationship. In particular, data item to be indexed is in theform <ui|uj , [tf , tu]>, where ui|uj is concatenation of apair of friends serving as the search key, and [tf , tu] is thevalid friendship period of ui and uj . Thus, TF-tree’s functionis to find which pairs of users are valid friends during thegiven time period, and the retrieval function can be representedas R=TFRetrv([tf , tu]), which means to retrieve pairs offriends associated with corresponding valid time period during[tf , tu].

V. QUERY PROCESSING

In this section, we handle the query processing for TGQ.First we propose a straightforward approach, after that, weoptimize it to improve the efficiency.

A. Naive Searching

For a TGQ (W , [ts, te], tol), the basic workflow is asfollowing: firstly, TA-tree is used to retrieve the user set (sayUc) participating in the activities containing the keyword setW during [ts, te], then for each candidate user ui in Uc,sum of on-line duration during [ts, te] is calculated. Then, thedifficulty lies in how to return the satisfied group with validtime period. Through observation, we get that the group’s validperiod depends on each relationship’s changing time, e.g., atemporal interval for a relationship is [tf , tu], which wouldcontribute the valid period of the group. Thus we can use TF-tree to retrieve all pairs of friends during [ts, te], say Fc, andwe can generate pairs of friends in Uc associated with validtime period by intersecting Uc and Fc, after that, for each time

point when friendship change happens in Uc, we calculate thesatisfied snapshots of groups (i.e., connected graph), and thenform the results.

For accelerating the processing, we use a max-queue storingusers in Uc sorted by on-line duration, thus we can terminatethe loop as early as possible. In particular, on each time pointti, we calculate a set of snapshot connected graph whose AODis larger than or equal to tol, i.e., top element utop of the max-queue is popped and checked whether on-line duration is notless than tol, if so, that is to say it is possible for finding asatisfied connected graph containing utop, then a connectedgraph Gti on time t is generated, and check whether AOD ofGti is larger than or equal to tol, if so, Gti is a result, afterthat, all users in Gti are removed from the queue, and nexttop element is popped and the similar processing is continued.Otherwise, i.e., on-line duration of utop is less than tol, whichmeans it is impossible to find a satisfied connected graph forthe elements following utop, so the loop for the queue isterminated and processing is moved to the next time point.Algorithm 1 presents the pseudo-code of naive searching.Algorithm 1 Naive SearchingInput: q=(W , [ts, te], tol)Output: Rlist1: Uc=TARetrv([ts, te], W )2: Q=generateQueue(Uc)3: Fc=TFRetrv([ts, te])4: TP=extractT imePoints(Fc, Uc)5: for each tp ∈ TP do6: replQ=Q7: while replQ 6=φ do8: u=dequeue(replQ)9: if u.od≤tol then

10: CQ=geneCQ(u, tp)11: if AOD(CQ)≤tol then12: Rlist←(CQ, tp)13: end if14: else15: break16: end if17: end while18: end for19: return Rlist

For example, after retrieving the users that satisfied thekeywords and time constristant, Uc={u1,u2,...,u15} is found,and tol=300. The relationships between these users, Fc isshowed in Figure 3 with time interval tags. Meanwhile, atimeline containing ti, and the sum of on-line duration of eachui is also showed in this figure.

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Fig. 3. Example of TGQ

As shown in Figure 4, on time t1=300, utop = u6 (showin bold), we form a connected graph for u6, and then checkthat AOD=382>300, so we add it to the result list. Andthen {u6, u3, u10, u15, u13} are removed. utop changes to u9,we simply form a a connected graph for u9, and checkthat AOD=291.7<300, this result does not satisfy. Until theutop = u2, the on-line duration of u2=300, is not less than tol.So the processing is jumped to the next time point t2=400. Dueto space limitations we do not show the processing at time 500and 800.

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Fig. 4. Naive Searching Example

B. Optimized ProcessingWe optimize the naive searching in this section, through

observation, we can see that, it is not necessary to constructconnected graphs at each time point. On the contrary, all theconnected graphs can be constructed initially, and at each timepoint, according to the changes of relationship, we updatethe corresponding graph and make judgment whether it is asatisfied group. In particular, we argue that the key techniqueslie in the update operations to connected graphs. On each timepoint, there are one or more operations to previous connectedgraphs, and we distinguish the following cases:

(1) Addition of relationship between nodes both in a con-nected graph cg. For this case, no judgment need to make, i.e.,the results are the same with the previous step.

(2) Addition of relationship between a node in a connectedgraph and an isolating node inode. For such a case, a newconnected graph containing inode is generated, which shouldbe inspected whether it is a satisfied group, i.e., whetheraverage on-line duration is not less the given value.

(3) Addition of relationship between two isolating nodes.For such a case, a new connected graph is formed, theprocessing is the same with case (2).

(4) Addition of relationship between one node in a con-nected graph and the other node in another connected graph.For such a case, a new connected graph is formed, theprocessing is the same with case (2).

(5) Removal of relationship between two nodes, resultingno split in a connected graph. For this case, no judgment need

to make, and results are unchanged.(6) Removal of relationship between two nodes, resulting

a connected graph split. For this case, the two emergingconnected graphs should both be inspected whether they arestill satisfied groups.

Unlike the naive searching, the optimized processing onlyconsider the changes of relationship in the graph, also takeFigure 3 as an example, the processing is shown in Figure5. Firstly, we form connected graphs at t1=300. Then att2=400, the changes of relationship are addition of relationship{u4,u13} (case 2) and {u3,u10} (case 1). Adding the relation-ship {u3,u10} in case 1 have no effect on the previous step,while adding the relationship {u4,u13}, a new connected graphis formed. In this case, a new member u4 (on-line durationis 160) is added to Gt1 in time 300 which results to AODchanging and Gt1 is no longer the satisfied result. At t3=500,the changes of relationship are establishment relationship{u1,u14} (case 3) and {u9,u10} (case 4). At t4=800, thechanges of relationship are removal of relationship {u3,u10}(case 5) and {u13,u15}, {u9,u11} (case 6).

VI. EXPERIMENTAL EVALUATION

We implement the indexes and processing algorithms,and experimentally evaluate them on a synthetic-real-hybriddataset. Due to the fact that there is no real dataset contain-ing temporal information on on-line status, relationship andactivity participation. Thus we have to synthetically generatedataset based on some real datasets which contain partialtemporal attributes. Table I lists some properties of thesedatasets. Datasets Users is generated according to the caseof YouTube, which owing 3,223,589 users. Then accordingto birthday information of Users, we randomly produced thelogin time list of each user, which forms the login dataset.Datasets Relation is produced based on the real dataset1,which contains 9,375,374 pairs of relation of YouTube. Forthe dataset of Activity, firstly, we download the dataset aboutfood theme on GCZX server, formed in xml file of 25 classesof Amazon commodities, 1759 review on the hotel and someweb crawling data, etc. Secondly, we extract the useful textas part of the text of activity, and randomly generated userswho involved in this activity and the time participate in theactivities.

TABLE IDATASET DESCRIPTION

Dataset Record number Data size

User 3,223,589 287M

Relation 9,375,374 5.53G

Login 3,223,589 2.45G

Activity 6,980,465 2.28G

We implement our algorithms in Java. To make comparison,the naive searching approach is used as a baseline. We varythe query parameters and at each testing point, 10 queriesare issued to collect the average results. The experiments areconducted on a DELL server with Intel(R) Xeon(R) 2.40GHz

1http://konect.uni-koblenz.de/downloads/tsv/youtube-u-growth.tar.bz2

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T=500 +(u1,u14) +(u9,u10)

u6

u3u8

u1

u2

u4

u5

u9

u11

u10

u12

u13

u14

u15

u7 u7

T=800 -(u13,u15) -(u3,u10)-(u9,u11)

u6

u3u8

u1

u2

u4

u5

u9

u11

u10

u12

u13

u14

u15

u7

g1={u6,u3,u10,u15,u9,u8}

Avg=382 Avg=291.7

Avg=190

Avg=216.6 Avg=271.6

Avg=190

Avg=291.7

Avg=197.5

Avg=331.6

Avg=197.5

Avg=190

Avg=215

Avg=190

Fig. 5. Optimized Processing Example

processor, 8GB memory and 500GB disk. Table II describesthe query parameters.

TABLE IIPARAMETERS IN EXPERIMENT

queries parameters domain defualt

TGQ

tol 1 - 5 3

Wq’s cardinality 1 - 5 3

length[ts,te]/temporal extent 0.1%-3% 1%

Firstly, we vary tol to compare the performances of twoalgorithms. We increase tol from 1 to 5, while the responsetime of query decreases (see Figure 6(a)), this is due to ourterminating condition, i.e., a larger tol will terminate loopearlier, thus the processing delay is reduced. For the detail,we can see the effectiveness of our optimization, i.e., theoptimized approach utilizes the updates to the graphs, whichreduces the simple repeated group forming procedure, thus itcost less time to retrieve the results.

Next, we increase the number of querying keywords to testperformances. We can see from Figure 6(b), the responsetime also increases with the number of keywords. This canbe explained that a larger number of keywords would involvemore tree nodes in the TA-tree to be traversed, thus more timewould be cost. Similarly, the optimized approach outperformsthe naive searching.

Figure 6(c) illustrates the results of varying parametertime selectivity, a larger value causes more candidates to beinspected, thus the response time increases correspondingly.And still, the results show that a series of update operationsis more efficient than exhausted method.

VII. CONCLUSION

With applications continuously developing, more and moretemporal social network group queries will be paid attention.In this paper, we focus on temporal analytics on social groupquery, and argue Temporal Group Query (TGQ) is useful andapplicable. To efficiently address the query, we design twoindexing structures to accelerate the query processing, and twoprocessing algorithms, one is simple, the other is optimized, toaccomplish the processing. We conduct experiments on real-synthetic hybrid dataset, and the results show our methods arecapable and optimized method is efficient. In the future, wewould like to study on social group query with geographicattributes.

1 2 3 4 5

0

5000

10000

15000

20000

25000

30000

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lay(

ms)

Average On-line Duration

Naive

Optimized

(a) Effect of tol

1 2 3 4 5

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6000

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ms)

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

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(c) Effect of time selectivity

Fig. 6. Experimental Results

ACKNOWLEDGMENT

This work is supported by NSF of China grant 61303062and 61302144. We would like to thank Prof. Dai and Dr. Hufor helping with the proof.

REFERENCES

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