Dazhong Wu1

Department of Industrial and

Manufacturing Engineering,

Pennsylvania State University,

University Park, PA 16802

e-mail: dxw279@psu.edu

David W. RosenThe G.W. Woodruff School of

Mechanical Engineering,

Georgia Institute of Technology,

Atlanta, GA 30332

e-mail: david.rosen@me.gatech.edu

Jitesh H. PanchalSchool of Mechanical Engineering,

Purdue University,

West Lafayette, IN 47907

e-mail: panchal@purdue.edu

Dirk SchaeferDepartment of Mechanical Engineering,

University of Bath,

Bath BA2 7AY, UK

e-mail: d.schaefer@bath.ac.uk

Understanding Communicationand Collaboration in SocialProduct Development ThroughSocial Network AnalysisSocial media have recently been introduced into the arena of collaborative design as anew means for seamlessly gathering, processing, and sharing product design-relatedinformation. As engineering design processes are becoming increasingly distributed andcollaborative, it is crucial to understand the communication and collaboration mecha-nism of engineers participating in such dispersed engineering processes. In particular,mapping initially disconnected design individuals and teams into an explicit social net-work is challenging. The objective of this paper is to propose a generic framework forinvestigating communication and collaboration mechanisms in social media-supportedengineering design environments. Specifically, we propose an approach for measuring tiestrengths in the context of distributed and collaborative design. We transform an implicitdesign network into an explicit and formal social network based on specific indices of tiestrengths. We visualize the process of transforming customer needs to functional require-ments, to design parameters, and to process variables using social network analysis(SNA). Specifically, by utilizing a specific index for tie strengths, we can quantitativelymeasure tie strengths in a design network. Based on the tie strengths, we can map animplicit design network into an explicit social network. Further, using the typical meas-ures (e.g., centrality and cluster coefficient) in SNA, we can analyze the social network atboth actor and systems levels and detect design communities with common design inter-ests. We demonstrate the applicability of the framework by means of two examples. Thecontribution in this paper is a systematic and formal approach that helps gain newinsights into communication and collaboration mechanisms in distributed and collabora-tive design. [DOI: 10.1115/1.4031890]

Keywords: communication and collaboration mechanism, collaborative design, socialproduct development, social networking analysis, tie strength, design network

1 Introduction

As engineering design activities are conducted in an increas-ingly distributed and collaborative setting, individual designers ordesign teams at different locations need to communicate and col-laborate effectively and efficiently [1–3]. T€orlind and Larsson [4]described engineering design as “fundamentally a sociotechnicalactivity” in which engineers gather, process, and share informa-tion about customer needs, function requirements, design parame-ters, and process variables as well as make collective decisions inorder to satisfy customer needs. As social media have the potentialto enhance communication and collaboration in design, socialproduct development (SPD) has emerged as a new trend toimprove traditional distributed and collaborative design processes[5–7]. The objective of SPD is to enhance communication andcollaboration in distributed and collaborative design throughsocial computing techniques such as social networking sites andonline communities.

Although research related to SPD is in its infancy, companiesare piloting social media initiatives to generate business value inthe field of design and manufacturing. One of the most well-known industry practices is Yammer [8], a so-called “Facebookfor the workplace.” Yammer is a platform designed to streamlinecommunication and collaboration processes by bringing togetherpeople, content, and conversations across entire product

development processes. Another example is Quirky [9], an indus-trial design company that utilizes a social media site to bring inno-vative product ideas to real life. Quirky allows designers anddesign teams to conduct engineering design modeling and analysisby using cloud-based computer-aided design and finite elementanalysis tools such as Dassault Systems’ CATIA V6. Meanwhile,Dassault Systems also introduced an online SPD platform,3DswYm [10], for sharing design-related information and experi-ences via commonly used social media tools such as wikis andblogs. In addition, General Electric (GE) and Massachusetts Insti-tute of Technology (MIT) are developing a new crowdsourcingplatform [11] to support DARPA’s ongoing adaptive vehiclemake portfolio. Their crowdsourcing platform allows a globalcommunity of experts to design and rapidly manufacture complexindustrial products and systems such as aviation systems by con-necting individuals in an online community.

Because of the increasing number of design participants andteams involved in a SPD process, it is crucial to increase the effec-tiveness and efficiency of design communication and collaboration.The engineering management literature shows that effective and ef-ficient communication and collaboration is one of the most impor-tant success factors that affect productivity, lead-time, and costs.Dong [12] reveals that almost all successful product design teamshave high levels of communication and collaboration becauseseamless information sharing supports the creation of a sharedunderstanding of engineering problems between engineers. McKin-sey [13] suggests that a “well-connected” design network plays acritical role in the decision-making process of marketing, concep-tual, embodiment, and detail design phases based on their recentsurvey. However, the challenge in understanding communication

1Corresponding author.Contributed by the Design Engineering Division of ASME for publication in the

JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscriptreceived March 7, 2014; final manuscript received October 22, 2015; publishedonline December 10, 2015. Editor: Bahram Ravani.

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and collaboration mechanisms lies in mapping distributed and col-laborative design teams into a network as well as capturing the pro-cess of transforming customer needs to functional requirements, todesign parameters, and to process variables as shown in Fig. 1.

In the context of engineering design, the purposes of under-standing information flow include the following two aspects:

� to analyze the transformation of information among productmodules that share design variables [14–19]

� to analyze the transformation of information among individu-als or design teams at different design phases (e.g., conceptdesign and embodiment design) [20–22]

This paper is focused on the second aspect because of the socio-technical nature of engineering design processes as stated before.

While some qualitative studies suggest how human and organi-zational systems could be restructured to improve productivity[23], only few investigate how information transformation in adesign process can be formally modeled and analyzed in a quanti-tative way. Although SNA has been used to study interfirm rela-tionships of interconnected buyers and suppliers in supply chainmanagement [24], few studies apply SNA in the context of engi-neering design. In particular, there has been limited study ofmeasuring tie strengths between engineers and mapping initiallydisconnected individuals and teams in a design network into asocial network in the context of distributed and collaborativedesign. This is largely because (1) there is no formal frameworkfor investigating communication and collaboration mechanisms indistributed and collaborative design; (2) there is a lack of clarifica-tion with respect to indices for measuring tie strengths betweenindividuals or design teams; and (3) it is still very challenging toconduct large-scale real-world industrial case studies. The objec-tive of this paper is to address the first two issues as a first step to-ward understanding communication and collaborationmechanisms in SPD settings.

The remainder of the paper is organized as follows: Section 2presents a brief overview of communication and collaboration inengineering design as well as related aspects of SNA. Section 3presents a generic framework for investigating communicationand collaboration with a focus on measuring tie strengths andsocial networks in the context of distributed and collaborativedesign. Section 4 presents the validation of the framework bymeans of two engineering design sample problems. In these appli-cation examples, we formally map two implicit design networksinto two explicit social networks and analyze the social networksusing some of the typical measures in SNA such as degree, graphdensity, betweenness centrality, closeness centrality, and cluster-ing coefficient. In addition, we analyze and interpret the results ofour SNA. The results include visualized information flow, net-work structures, and detected collaboration patterns. Section 5concludes this paper with a discussion of our research contribu-tions and associated limitations.

2 Literature Review

As previously stated, although some qualitative studies suggesthow sociotechnical systems could be restructured to improve theeffectiveness and efficiency of communication, only few investi-gate how complex design networks can be formally mapped intosocial networks [25–27]. Specifically, the following two research

issues have not yet been fully addressed: (1) What indices formeasuring tie strengths between designers should be used in thecontext of design? (2) How can the transformation of customerneeds to functional requirements, to design parameters, and toprocess variables be visualized and analyzed in a formal way? Inorder to address these issues, this paper builds upon prior work intwo areas: (1) qualitative studies in engineering communicationand collaboration and (2) SNA in communication and collabora-tion. We provide a brief review of the related work in the abovetwo areas in Secs. 2.1 and 2.2.

2.1 Communication and Collaboration in EngineeringDesign. According to Refs. [28–31], the major purposes of designcommunication include articulating an issue, asking for clarifica-tion, eliciting requirements, generating concepts or principles,reverse engineering, requesting information, comparing solutions,and making decisions. Capturing the purposes of design commu-nications can significantly improve the effectiveness and effi-ciency of design communication by ensuring that engineers knowwhat expected inputs and outputs should be from a communica-tion. With respect to the content or artifacts that are exchanged orshared among individuals or teams, almost all design communica-tions revolve around artifacts including sketches, engineeringdrawings, computer-aided design files, simulation, finite elementanalysis files, physical product, calculation, assembly, prototype,and report [31]. According to Henderson [32], among these arti-facts, sketches, engineering drawings, and finite element analysisfiles are perhaps the most fundamental components of engineeringdesign communication in most design contexts. In order to effec-tively and efficiently support design communication, Gopsill et al.[31] have synthesized the requirements of effective design com-munication from the review of literature. Some of the most impor-tant requirements include: (1) to enable individuals to haveubiquitous access to design-related data, (2) to enable individualsto communicate via multiple channels such as virtual meetingsand text messages, (3) to enable individuals to record changes toan artifact as a consequence of a communication, (4) to enableindividuals to share text-based descriptions of an artifact, (5) toenable individuals to share electronic references to an artifact, and(6) to enable individuals to solicit responses (e.g., surveys andpolls) from one another. However, few studies investigate how toenhance communication and collaboration in engineering designin a quantitative way.

2.2 SNA for Communication and Collaboration. Becausesocial media play an important role in supporting communicationand collaboration in a sociotechnical environment, SNA providesboth a visual and a mathematical analysis of communicationand collaboration relationships between individuals [33,34].Haythornthwaite [35] introduced SNA as an explicit approach andset of associated techniques for the study of informationexchange. Jensen and Neville [36] studied SNA using machinelearning and data mining techniques and developed methodsfor constructing statistical models of network data. Kim andSrivastava [37] presented an overview of the impact of socialinfluence in e-commerce and suggested key issues to focus on,including how to combine social influence data into user preferen-ces, and how to exercise social influence in the context of custom-ers’ purchase decision making. Borgatti and Li [38] discussed the

Fig. 1 Typical information flow in engineering design processes

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potential of SNA for supply chain management by applying net-work concepts to both hard (e.g., material and money flow) andsoft (friendships and sharing-of-information) types of ties. Glooret al. [39] introduced a novel set of SNA-based algorithms formining the web, blogs, and online forums to identify trends andfind the people launching these new trends. Lin et al. [40] devel-oped a social networking application, SMALLBLUE, which unlocksthe valuable business intelligence of “who knows what?,” “whoknows whom?,” and “who knows what about whom?” within anorganization. Their goal was to locate knowledgeable colleagues,communities, and knowledge networks in companies. Hassan [41]demonstrated how SNA theory supports the task of designinginformation technology (IT)-enabled business processes by pro-viding social network metrics for evaluating alternative processdesigns. These metrics offer better information for process design-ers who are faced with making IT investment tradeoffs, especiallyas the process design task is being undertaken. Braha and Bar-Yam [42] analyzed the statistical properties of real-world net-works of people involved in product development activities andshowed that complex product development networks exhibit the“small-world” property, meaning that the actors can be reachedfrom anywhere by a small number of steps. Despite the literatureas mentioned above has investigated product development from asocial process perspective, little is known about the potential of theSNA to investigate the information flow and collaboration patternsin engineering design. Especially, the research gap is that few stud-ies are conducted to identify potential metrics for measuring the ex-istence of connections between participants in engineering design.Without formal measures for relationships between individuals inthis context, the linkages in social networks are neither rigorous noraccurate.

As part of the SNA, the aim of community detection is to (1)detect organizations or individuals with similar interests and (2)create data structures to handle queries or path searches [43]. Themodern science of graph theory has brought significant advancesto our understanding of complex networked systems. One of themost relevant features of graph theory is community detection orclustering, i.e., the organization of vertices in clusters, with manyedges joining vertices of the same cluster and with comparativelyfewer edges joining vertices of different clusters [44]. Girvan andNewman [45] proposed an algorithm aiming at the identificationof edges lying between communities and their successiveremoval, a procedure that after some iterations leads to the isola-tion of the communities. In this seminal work, the intercommunityedges are detected according to the values of a centrality metrics,and the edge betweenness that expresses the importance of therole of the edges is transmitted across the graph following thepaths of minimal length. Identifying clusters of customers withsimilar interests in the network of purchase relationships betweencustomers and products of online retailers, like Amazon, enablesus to set up efficient recommendation systems [46], which betterguide customers through the list of items of the retailer and helpcompanies to improve their sales and profitability. Tyler et al.[47] developed a methodology for the automatic identification ofcommunities of practice from e-mail logs by using the between-ness centrality algorithm. This approach enables the identificationof leadership roles within the communities. Clauset et al. [48]developed an algorithm for inferring community structure from

network topology, which is applied to analyze a large network ofco-purchasing data from Amazon.com. The research gap betweenthe SPD and SNA is that few studies investigate the measurementof tie strengths and validate the potential of the SNA on under-standing communication and collaboration in engineering design.To bridge the gaps we identified in Secs. 2.1 and 2.2, we introducea systematic framework for measuring tie strengths and gaininginsights into effective and efficient communication and collabora-tion in SPD settings.

3 A Framework for Investigating Design

Communication and Collaboration

In this section, we propose a generic SNA-based framework forinvestigating design communication and collaboration in SPD set-tings. The potential users of the framework include systems ana-lysts and users of SPD platforms. A systems analyst monitors theexchange of data between designers participating in a distributedand collaborative design process and evaluates the performance ofdesign communication and collaboration. For example, a systemsanalyst tracks data such as electronic files (e.g., computer-aideddesign and finite element analysis files) that are shared amongdesigners. Based on these data, the systems analyst defines anindex to measure tie strengths between two individuals or designteams. Based on the values of the index, one can map an implicitdesign network into an explicit and formal social network. Onecan further formally analyze the social network by utilizing typi-cal SNA measures (e.g., centrality and cluster coefficient). Then,the social network can be visualized and further analyzed withcommunity detection algorithms that capture the informationflow, identify key design participants, also referred to as actors,and detect design communities with common interests. Based onthese results, the systems analyst can identify potential communi-cation and collaboration problems through strong and weak tiesaccordingly. The detailed steps of the SNA framework are pre-sented in Table 1. The key steps of the framework, steps 1 and 3,are discussed in more detail in Secs. 3.1 and 3.2, respectively.

3.1 Measuring Tie Strengths. Social network data are typi-cally gathered through questionnaires and interviews in which theactors are asked to identify the frequency of communication withothers as well as mediums of interaction. It is commonly agreedthat social network data collected through questionnaires andinterviews are not perfectly accurate due to the fact that responsesare subjective in nature. Gupte and Eliassi-Rad [49] introduced anaxiomatic approach of measuring tie strength between actors insocial networks. A list of axioms is used to evaluate specific meas-ures of tie strengths between two actors. We extend that line ofwork by studying specific indices for tie strengths in the contextof distributed and collaborating engineering design. In this sec-tion, we review some of the axioms that can help clarify the indexthat will be used in our application examples in Sec. 4.

AXIOM 1 (ISOMORPHISM): Suppose we have two graphs G and Hand a mapping of vertices such that G and H are isomorphic. Letvertex u of G map to vertex a of H and vertex v to b. Then, the tiestrength between u and v in the graph G, denoted by TSGðu; vÞ, isequal to the tie strength between a and b in the graph H, denoted

Table 1 The SNA framework

SNA for SPD

1. Define an index to measure tie strength, that is, to determine whether the ties between the actors exist and to what degree the actors are connectedto one another

2. Collect raw data about actors and ties between actors for mapping an implicit social network into an explicit social network3. Calculate the measures (e.g., centrality and cluster coefficient) of the explicit social networks4. Visualize the social network, capture information flow, and detect key actors and communities with common design interests5. Interpret results and identify potential solutions for enhancing communication and collaboration

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by TSHða; bÞ. This relationship can be formally denoted byTSGðu; vÞ ¼ TSHða; bÞ. In the context of engineering design,design teams A and B can be represented by two graphs G and H,respectively. Two engineers in design team A can be representedby two vertices u and v in the graph G. Similarly, another twoengineers in design team B can be represented by two vertices aand b in the graph H. Axiom 1 suggests that the tie strengthbetween the two engineers in design team A is equal to the tiestrength between the two engineers in design team B if G and Hare isomorphic.

AXIOM 2 (BASELINE): If there are no events (an event is definedas a circumstance participated by a set of individuals for a certainpurpose), then the tie strength between vertices u and v in thegraph, denoted by TSøðu; vÞ, is equal to zero. This is formallydenoted by TSøðu; vÞ ¼ 0. If there are only two actors u and v anda single event they attend, then their tie strength, denoted byTSfu;vgðu; vÞ, is equal to one. This is formally denotedby TSfu;vgðu; vÞ ¼ 1. In the context of engineering design, Axiom2 suggests that the tie strength between any two engineers in adesign team is equal to zero if the two designers do not participatein any design-related events. This axiom also suggests that the tiestrength between two engineers in a design team is equal to one ifthere are only two engineers in the design team and they onlyattend one single design-related event.

AXIOM 3 (FREQUENCY): All other things being equal, the moreevents common to u and v, the stronger the tie strength isbetween u and v. In the context of engineering design, Axiom 3suggests that the tie strength between two engineers in a designteam will be greater if they share more common design-relatedevents and all other conditions remain the same.

AXIOM 4 (INTIMACY): All other things are being equal, thefewer actors there are to any particular event attended by uand v, the stronger the tie strength is between u and v. In thecontext of engineering design, Axiom 4 suggests that the tiestrength between two engineers in a design team will be greaterif fewer engineers participate in the common design-relatedevents they share. In fact, Axiom 4 is a special case of Axiom 2.The special case is that the tie strength between two engineersin a design team is equal to one if there are only two engineersin the design team and they only attend one single design-related event.

AXIOM 5 (POPULARITY): Consider two events P and Q. If thenumber of actors attending P is larger than that of actors attend-ing Q, then the total tie strength created by event P is more thanthat created by event Q. In the context of engineering design,Axiom 5 suggests that the total tie strength created by a particulardesign-related event P is more than that created by another one Qif more engineers participate in event P.

AXIOM 6 (CONDITIONAL INDEPENDENCE OF VERTICES): The tiestrength of a vertex u to other vertices does not depend on eventsthat u does not attend; it only depends on events that u attends. Inthe context of engineering design, Axiom 6 suggests that the tiestrength of an engineer to others does not depend on the design-related events that this engineer does not attend.

AXIOM 7 (CONDITIONAL INDEPENDENCE OF EVENTS): The increase intie strength between u and v due to an event P does not depend on

other events but on the existing tie strength between u and v. Inthe context of engineering design, Axiom 7 suggests that theincrease in tie strength between two engineers does not depend onother design-related events.

AXIOM 8 (SUBMODULARITY): The marginal increase in tiestrength of u and v due to an event Q is at most the tie strengthbetween u and v if Q was the only event. If G is a graph and Q is asingle event, then TSGðu; vÞ þ TSQðu; vÞ � TSGþQðu; vÞ. In thecontext of engineering design, Axiom 8 suggests that the marginalincrease in tie strength between two engineers due to a commondesign-related event they share is at most the tie strength betweenthe two engineers if this event is the only one they attend.

According to Gupte and Eliassi-Rad [49], although plenty ofgeneric measures of tie strength exist and each of the axioms isfairly intuitive, only some of the well-accepted measures of tiestrength satisfy all the aforementioned axioms. These measuresinclude (1) delta, (2) Adamic and Adar, (3) linear, and (4) max.The detailed and formal proofs can be found in Ref. [49]. In thefollowing indices, jPj denotes the number of actors in the eventP. The size of the neighborhood of a vertex u in a graph is

denoted by CðuÞ. The tie strength between two vertices u and vin a graph is denoted by TSðu; vÞ.

The delta index defines tie strength as

TS u; vð Þ ¼X

P2C uð Þ\C vð Þ

1

jPj2

� �

The Adamic and Adar index defines tie strength as [50]

TS u; vð Þ ¼X

P2C uð Þ\C vð Þ

1

log jPj

The linear index defines tie strength as

TS u; vð Þ ¼X

P2C uð Þ\C vð Þ

1

jPj

The max index defines tie strength as

TS u; vð Þ ¼ maxP2C uð Þ\C vð Þ

1

jPj

Based on these formally defined tie strengths, we can formallymap an implicit design network into an explicit social network.The following simple example illustrates that how we can map adesign network into a social network based on tie strengths inmore detail. Table 2 lists five actors and the events they attended.These events include sharing a particular digital file (denote byP1), making comments on a particular post (denote by P2), partic-ipating a particular virtual meeting (denote by P3), a particularvirtual conference call (denote by P4), and a particular poll(denote by P5). Given the dataset in Table 2, we can map animplicit design network into an explicit social network (seeFig. 2) based on the Adamic and Adar index scores.

Table 2 Adamic and Adar index scores

Connections

Actor ID Actor ID No. of actors in P1 No. of actors in P2 No. of actors in P3 No. of actors in P4 No. of actors in P5 Adamic and Adar index

1 2 3 3 0 0 0 4.19181 3 3 3 0 0 0 4.19181 4 0 0 3 2 0 5.41782 3 3 3 0 0 0 4.19184 5 0 0 3 0 2 5.4178

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3.2 Measuring Social Networks. The next step of the frame-work is to analyze the explicit social network using the followingmeasures at both actor and group levels. We first define somecommonly used measures from SNA that help clarify the uses ofthese measures in the application examples in Sec. 4.

Degree: Degree of a vertex of a network is the number of edgesincident to the vertex. In this study, degree gauges how many con-nections a particular actor possesses. A higher degree reflectsmore connections that an actor is tied to. In contrast, an actor withlow degree is considered peripheral in a social network. Further,degree also refers to the extent to which an actor influences otheractors with respect to the sharing-of-information and decisionmaking, as the actor has more direct connections thereby morelikely having more critical information that others may not knowabout. For instance, a subgroup leader in a distribute design teamwill more likely have a higher degree as this leader is in a positionthat calls for meetings, gathers information from other groups tohis group members, and delivers information from his groupmembers to other groups.

Graph Density: Graph density is the average of the standardizedactor degree indices as well as the fraction of possible ties presentin the network for the relation under study. In other words, itmeasures how many edges in a network compared to the maxi-mum possible number of edges. Graph density takes on valuebetween zero (empty graph) and one (complete graph).

Betweenness Centrality: Betweenness defines the extent towhich an actor lies between other actors in a network. This mea-sure takes into account the connectivity of the actor’s neighbors,giving a higher value for actors which bridge clusters. This mea-sure also indicates the number of actors which the actor is con-nected to indirectly through the direct links [51].

Actor betweenness centrality is defined as

C0B nið Þ ¼CB nið Þ

g� 1ð Þ g� 2ð Þ=2� �

where C0BðniÞ is the standardized actor betweenness index for ni.CBðniÞ is the actor betweenness index for ni. g is the number ofactors. The calculation of CBðniÞ is discussed in more detail inRef. [41].

Group betweenness centrality is defined as

CB ¼2Xg

i¼1

CB n�ð Þ � CB nið Þh i

g� 1ð Þ2 g� 2ð Þh i

where CB is the index of group betweenness. CBðn�Þ is the largestrealized actor betweenness index for the set of actors.

In this paper, betweenness can be viewed as an indication ofhow much “gatekeeping” an actor does for the other actors. Itmeasures how important the actor is with respect to the flow ofinformation. An actor with high betweenness can control the flowof information as the actor functions as a hub or pivot that trans-mits information across the network. Further, from the structuralposition perspective, the actor with high betweenness is morelikely one of the key actors in the network as the actor affects thedownstream actors’ access to information from upstream actors.For instance, in a design network, the structural position ofdesigners is between market analysts and manufacturing engineers

as designers transform function requirements to design parame-ters. Therefore, designers become a hub between market analystsand manufacturing engineers. If a designer with high betweennesstransmits design-related information slowly or delivers somewrong information, the design becomes the bottleneck of theinformation flow in the network. As a result, the gap in the infor-mation flow can easily lead to poor communication andcollaboration.

Closeness Centrality: Closeness centrality defines the degree towhich an actor is near all other actors in a network. This measureindicates the ability to access information through the grapevineof network members. In other words, the closeness indicates howquickly an actor accesses the information from the network.Closeness centrality is the inverse of the sum of the shortest dis-tance between each actor and every other actor in the network.

Actor closeness centrality is defined as

C0C nið Þ ¼g� 1Xg

j¼1

d ni; njð Þ" #

where C0CðniÞ is the standardized index of actor closeness.dðni; njÞ is the number of lines in the geodesic linking actors i andj. The details about how to calculate dðni; njÞ can be found inRef. [51].

Group closeness centrality is defined as

CC ¼

Pgi¼1

C0C n�ð Þ � C0C nið Þh i

g� 2ð Þ g� 1ð Þ½ �= 2g� 3ð Þ½ �

where CC is the index of group closeness. C0Cðn�Þ is the largeststandardized actor closeness in the set of actors.

Clustering Coefficient: Clustering coefficient of an actor is theratio of number of connections in the neighborhood of an actorand the number of connections if the neighborhood was fully con-nected. Clustering coefficient identifies how well connected theneighborhood of an actor is. If the neighborhood is fully con-nected, the cluster coefficient is one. A value close to zero meansthat there are hardly any connections in the neighborhood of theactor. A higher clustering coefficient indicates a greater cliquish-ness [51]. In other words, it is the measure of the degree to whichnodes in a graph tend to cluster together. In the context of SPD,an actor with low cluster coefficient is more likely one of thegroup leaders as the neighborhood (group members) of the groupleader is generally fully connected.

4 Application Examples

In this section, we present two application examples to demon-strate how the proposed framework can help understand designcommunication and collaboration mechanism in SPD settings. Inour application examples, actors are engineering graduate studentsin an engineering design class. This class was composed of bothon-campus and distance learning students. We required these stu-dents to design two mechanical product prototypes in an SPDenvironment which consisted of a variety of social media tools(e.g., Wiggio, Google Drive, and others). Design activities inthese design projects involved the core phases of the systematicdesign approach by Pahl and Beitz starting from product planningand clarification of task, to conceptual design, embodimentdesign, and to detail design. The dataset of example 1 was col-lected in Spring 2011. There were 31 students in a class and thestudents were divided into two competing subgroups. The datasetof example 2 was collected from the Spring 2012 cohort. Therewere 39 students in a class and all the students teamed up to formone mass-collaborative group. The projects conducted in the twoexamples were: (1) example 1—designing a hydroelectric

Fig. 2 Map a design network into a social network based onAdamic and Adar index scores

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footwear (Spring 2011) and (2) example 2—designing a wind-based electricity generation device (Spring 2012).

We selected these application examples for two reasons. First,the two projects were conducted in an SPD environment where avariety of social media tools such as Wiggio, Google Drive, andDropbox were used to share design-related data. In addition, bothof the two projects were conducted in distributed and collabora-tive settings as shown in Fig. 3.

The on-campus students were located in Atlanta, Georgia, inthe U.S.; the distance learning students came from Georgia TechLorraine campus in Metz (France), Georgia Tech Savannah cam-pus, Flanders in New Jersey, Fairbanks in Alaska, Phoenix in Ari-zona, and Milwaukee in Wisconsin. Second, the projects in thetwo application examples were focused on engineering designproblems. The students were also required to build proof-of-concept prototypes to validate their design concepts using 3Dprinting technology. Therefore, these two design scenarios arevery similar to what happens in real-world cases from industry.

4.1 Measuring Tie Strengths. Based on the framework pre-sented in Sec. 3, step 1 is to define a specific index to measure tiestrength. Step 2 is to collect raw data about actors and ties thatcan map an implicit social network into an explicit social network.As stated in Sec. 3.1, according to Gupte and Eliassi-Rad [49],only four indices satisfy all of the axioms. We first measure tiestrengths in the application examples using these four indices andthen conduct a sensitivity analysis to test the effect of changes inthe number of events on the number of edges in the applicationexamples. The delta, max, linear, and Adamic and Adar indexscores for example 1 are shown in the Appendix. Although theindex scores for each connection based on these four indices aredifferent, the number of edges is identical. For example, the delta,max, linear, and Adamic and Adar index scores for measuring thetie strength between actors 1 and 2 are 28.0000, 0.3333, 28.0000,and 176.0559, respectively. Since all of the index scores aregreater than zero, an edge is identified between nodes 1 and 2 inthe social network. According to the Appendix, the same numberof edges, 51, is identified based on these four indices. Further, weconsider changes in the number of events (e.g., files, posts, meet-ings, calls, and polls) by �5% and �10%. As shown in Table 3,the number of edges we identified remains the same, 51.

According to the result of the sensitivity analysis, we found thatthese four indices are very robust.

Considering these four indices are all robust measures of tiestrengths, all of them are perhaps applicable. However, accordingto Shannon’s information theory and one of the two axioms in axi-omatic design (the information axiom), the most important quanti-ties of information are entropy, the amount of information incommon between two random variables. The entropy is mathe-matically expressed in the form of common logarithm. Becausethe Adamic and Adar index is also defined using common loga-rithm, this index intuitively includes the quantification of informa-tion that is shared in design communication. Therefore, we selectthe Adamic and Adar index to measure tie strengths in the applica-tion examples. The Adamic and Adar index scores for example 1is shown in the Appendix.

4.2 Measuring Social Networks. Based on the index scoresin the Appendix, we can map the implicit design networks intotwo explicit social networks. Step 3 is to calculate the measures(e.g., centrality and cluster coefficient) of the explicit social net-works. Step 4 is to visualize the social networks, capture informa-tion flow, and detect key actors and communities with commondesign interests. The major measures we used in these examplesinclude (1) vertices and edges, (2) degree, (3) graph density, (4)betweenness and closeness centrality, and (5) clustering coeffi-cient. We use an SNA tool, NODEXL, developed by Smith’s team atthe Microsoft Research [52] to perform steps 3 and 4.

The general network statistics, betweenness centrality, close-ness centrality, and clustering coefficient are listed in Tables 4and 5.

In example 1, eight actors (vertices 1, 4, 8, 15, 16, 20, 24, and28) are identified as the key actors in the information flow basedon their relatively high betweenness scores (see Table 6) in com-parison with the average betweenness score: 12.355 (see Table 5).

Moreover, two separate groups with eight clusters of actorswere successfully detected using the SNA as illustrated inFigs. 4(a) and 4(b). Group 1 was composed of vertices 16–31.Group 2 was composed of vertices 1–15. Four clusters weredetected for group 1. The information flow started with the prod-uct planning subgroup (vertices 28, 29, 30, and 31), to the conceptdesign subgroup (vertices 24, 25, 26, and 27), the embodiment

Fig. 3 Geographic locations of participating students

Table 3 Sensitivity analysis of indices for the number of edges in example 1

Number of edges in example 1

The number of events change by Delta index Max index Linear index Adamic and Adar index

�5% 51 51 51 51�10% 51 51 51 51

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design subgroup (vertices 20, 21, 22, and 23), and to the detaildesign subgroup (vertices 16, 17, 18, and 19). Similarly, anotherfour clusters were detected for group 2. Since groups 1 and 2 werecompetitive groups, there was no communication between them.As a result, the two groups were not connected with each other.

In example 2, the general graph metrics and statistics for groupcentrality are listed in the right two columns of Tables 4 and 5.Similarly, eight actors (vertices A, E, J, P, A1, G1, L1, and P1)are identified as the key actors in the information flow based ontheir relatively high betweenness scores (see Table 6) in compari-son with the average betweenness score: 27.000 (see Table 5).

Table 4 General network statistics in examples 1 and 2 at thegroup level

Example 1 Example 2

Graph metrics Value Graph metrics Value

Vertices 31 Vertices 39Total edges 51 Total edges 105Maximum vertices 16 Maximum vertices 39Maximum edges 27 Maximum edges 105Graph density 0.109 Graph density 0.143

Table 5 Centrality and clustering coefficient in examples 1 and 2 at the group level

Example 1 Example 2

Centrality Value Centrality Value

Minimum betweenness centrality 0.000 Minimum betweenness centrality 0.000Maximum betweenness centrality 68.000 Maximum betweenness centrality 165.000Average betweenness centrality 12.355 Average betweenness centrality 27.000Median betweenness centrality 0.000 Median betweenness centrality 0.000Minimum closeness centrality 0.021 Minimum closeness centrality 0.010Maximum closeness centrality 0.040 Maximum closeness centrality 0.016Average closeness centrality 0.026 Average closeness centrality 0.011Median closeness centrality 0.025 Median closeness centrality 0.010Minimum clustering coefficient 0.300 Minimum clustering coefficient 0.470Maximum clustering coefficient 1.000 Maximum clustering coefficient 1.000Average clustering coefficient 0.840 Average clustering coefficient 0.898Median clustering coefficient 1.000 Median clustering coefficient 1.000

Table 6 Network measures for vertices for examples 1 and 2 at the vertex (actor) level

Example 1 Example 2

Vertex Degree Betweenness Cluster coefficient Vertex Degree Betweenness Cluster coefficient

1 3 24.000 0.333 A 10 105.000 0.5334 5 57.000 0.300 E 11 136.000 0.4918 5 61.000 0.300 J 12 165.000 0.47015 4 33.000 0.500 P 10 105.000 0.53316 4 36.000 0.500 A1 12 165.000 0.47020 5 68.000 0.300 G1 11 136.000 0.49124 5 68.000 0.300 L1 10 105.000 0.53328 4 36.000 0.500 P1 11 136.000 0.491

Fig. 4 Community detection with Clauset–Newman–Moore algorithm [35]: (a) before commu-nity detection for example 1 and (b) after community detection for example 1

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Four clusters of actors were successfully detected for two sub-groups, A and B in a single team, respectively, as shown inFigs. 5(a) and 5(b). For subgroup A, the information flow startedwith product planning (vertices A, B, C, and D in orange), to con-cept design (vertices E, F, G, H, and I in red), embodiment design(vertices J, K, L, M, N, and O in light blue), and to detail design(vertices P, Q, R, and S in dark blue). Similarly, another four clus-ters were detected for subgroup B. Subgroups A and B were con-nected with each other through subgroup leaders of the team (i.e.,vertices A, E, J, P, A1, G1, L1, and P1) by utilizing some of theinformation sharing tools as described before.

4.3 Interpretation of Results. According to the frameworkin Sec. 3, step 5 is to interpret results and identify potential solu-tions for enhancing communication and collaboration. The gen-eral graph metrics in Table 5 and the statistics for centrality inTable 6 at the group level provide insights for understanding theoverall collaboration structure of the network. At the same time,some of the graph metrics at the actor (vertex) level are also veryvaluable to capture individual actors’ roles as shown in Table 6,including degree, betweenness centrality, and cluster coefficient.The following measures have been found to be important forunderstanding the overall collaboration structure:

� vertices, edges, and graph density� betweenness centrality, closeness centrality, and clustering

coefficient at the group level

Moreover, the results in Figs. 4 and 5 suggest that theClauset–Newman–Moore algorithm can detect the communitieseffectively. As illustrated in Figs. 4(a) and 4(b), theClauset–Newman–Moore algorithm identified eight actors inexample 1 who have relatively higher degree, betweenness cen-trality, and lower cluster coefficient at the actor level (as shown inTable 6) by comparing with the statistics for general metrics andcentrality at the group level (as shown in Tables 4 and 5). Wefound that the actors as shown in Table 6 (vertices 1, 4, 8, 15, 16,20, 24, and 28) are subgroup leaders who communicate with otheractors more often and have access to more information andresources. The same conclusion holds in example 2. As illustratedin Figs. 5(a) and 5(b), there are also eight subgroup leaders (verti-ces A, E, J, P, A1, G1, L1, and P1) but with higher betweennessand closeness centrality than those of subgroup leaders in example1 due to the fact that more communications (e.g., data exchange,file sharing, and online group discussion) between individualactors are enabled by the SPD systems. The following measures

have been found to be the most important for detecting commun-ities and key actors:

� degree� betweenness centrality and clustering coefficient at the actor

level

One of the main findings based on the results is that the com-munication and collaboration mechanisms in SPD settings can bevisualized and further be analyzed using the SNA. More specifi-cally, the implicit network structures for the two examples werevisualized using the SNA tool as shown in Figs. 4 and 5. Based onthe visualized network as well as the measures in SNA as shownin Tables 4–6, the structural positions of individual actors in thesocial networks were revealed, which helps gain sights into theeffectiveness of communication and collaboration in engineeringdesign. For instance, in example 1, the actors with ID 1, 4, 8, 15,16, 20, 24, and 28 as shown in Fig. 4 were identified as the criticalplayers who possess some of the significant design-related infor-mation as well as have better control over information flow. Inother words, these actors could also be the potential ones becom-ing the bottleneck of the flow of information in the network. Fur-thermore, consider group 2 in example 1, for example, theinformation flow that was detected turns out to be consistent withthat of the systematic design method by Pahl and Beitz, startingfrom the product planning (vertices 28, 29, 30, and 31 in darkblue), concept design (vertices 24, 25, 26, and 27 in light blue),embodiment design (vertices 20, 21, 22, and 23 in dark green),and to detail design (vertices 16, 17, 18, and 19 in light green). Asthe students are required to use the systematic design method byPahl and Beitz, the SNA framework is validated to be effectivefor capturing and measuring information flow in engineeringdesign processes in the context of SPD. Furthermore, individualswith common design activities were also detected. Based on thevisualized social networks and clusters, we can effectively iden-tify which designers are conducting similar design activities andwhere to find the information we may need.

With respect to collaboration patterns, we found that the SPDenvironments help enhance communication and collaborationamong participants as it transformed engineering design collabo-ration from a conventional sequential pattern into a parallel one asshown in Fig. 5. SPD allows designers to quickly access, edit, andshare product design-related information through a set of socialmedia tools. Due to the ubiquitous computing environment in theSPD, the sequence of interaction among individuals or designteams is not always unidirectional from planning, concept design,embodiment design, and to detail design. Instead, it could be

Fig. 5 Community detection with Clauset–Newman–Moore algorithm [35]: (a) before commu-nity detection for example 2 and (b) after community detection for example 2

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multiway interactions as detected in example 2. As shown in Fig.5, the actors with ID A, E, J, P, A1, G1, L1, and P1 are fully con-nected, which means the collaboration pattern is not a sequentialinteraction but concurrent information sharing among participants.Such a multiway interaction or parallel information sharing isvery desirable because different perspectives from different indi-viduals for the same information can enhance design for X (e.g.,manufacturability, reliability, and variety).

5 Conclusion

The research described in this paper contributes to the currentbody of knowledge in the sense that we introduced a genericframework for investigating communication and collaborationmechanisms in SPD settings. Specifically, we measured tiestrengths using four indices that satisfy all of the axioms in SNAand conducted a sensitivity analysis to test the robustness of thefour indices. Based on the result of the sensitivity analysis, weobserved that all of them are perhaps applicable. Because theentropy in Shannon’s information theory and axiomatic design isexpressed in the form of common logarithm and the Adamic andAdar index is also defined using common logarithm, we select theAdamic and Adar index to measure tie strengths in our examples.Based on the Adamic and Adar index scores, we transformedimplicit design networks into explicit and formal social networks.In our examples, we visualized the process of transforming cus-tomer needs to functional requirements, to design parameters, andto process variables using SNA. Using the typical measures in theSNA, we measured the social networks at both actor and systemslevels and detected design communities with common designactivities. This systematic and generic framework helps us gainnew insights into communication and collaboration mechanismsin SPD settings.

While the framework was validated using two examples, thelimitation of this study is acknowledged as follows. Our applica-tion examples were not conducted in the context of real industryenvironments but in a graduate level engineering design coursewhere different groups of student play different roles. Althoughthe projects conducted in the examples were to solve engineeringdesign-related problems, the working environment can only repre-sent the real industrial environment to a certain degree. Futurework will focus on conducting real industry case studies.

Appendix: Index Scores in Example 1

Connections

ActorID

ActorID

Deltaindex

Maxindex

Linearindex

Adamic andAdar index

1 2 28.0000 0.3333 28.0000 176.05591 3 28.0000 0.3333 28.0000 176.05591 4 6.0000 0.2500 9.0000 59.79472 3 28.0000 0.3333 28.0000 176.05594 5 16.8333 0.2500 25.2500 167.75744 6 16.8333 0.2500 25.2500 167.75744 7 16.8333 0.2500 25.2500 167.75744 8 6.0000 0.2500 9.0000 59.79475 6 16.8333 0.2500 25.2500 167.75745 7 16.8333 0.2500 25.2500 167.75746 7 16.8333 0.2500 25.2500 167.75748 9 15.6667 0.2500 23.5000 156.13068 10 15.6667 0.2500 23.5000 156.13068 11 15.6667 0.2500 23.5000 156.13068 15 6.0000 0.2500 9.0000 59.79479 10 15.6667 0.2500 23.5000 156.13069 11 15.6667 0.2500 23.5000 156.130610 11 15.6667 0.2500 23.5000 156.130612 13 17.8333 0.2500 26.7500 177.723212 14 17.8333 0.2500 26.7500 177.7232

Continued

Connections

ActorID

ActorID

Deltaindex

Maxindex

Linearindex

Adamic andAdar index

12 15 17.8333 0.2500 26.7500 177.723213 14 17.8333 0.2500 26.7500 177.723213 15 17.8333 0.2500 26.7500 177.723214 15 17.8333 0.2500 26.7500 177.723216 17 26.6667 0.2500 20.0000 132.877116 18 26.6667 0.2500 20.0000 132.877116 19 26.6667 0.2500 20.0000 132.877116 20 18.0000 0.2500 12.2500 81.387217 18 26.6667 0.2500 20.0000 132.877117 19 26.6667 0.2500 20.0000 132.877118 19 26.6667 0.2500 20.0000 132.877120 21 15.0000 0.2500 22.5000 149.486820 22 15.0000 0.2500 22.5000 149.486820 23 15.0000 0.2500 22.5000 149.486820 24 18.0000 0.2500 12.2500 81.387221 22 15.0000 0.2500 22.5000 149.486821 23 15.0000 0.2500 22.5000 149.486822 23 15.0000 0.2500 22.5000 149.486824 25 16.5000 0.2500 24.7500 164.435424 26 16.5000 0.2500 24.7500 164.435424 27 16.5000 0.2500 24.7500 164.435424 28 18.0000 0.2500 12.2500 81.387225 26 16.5000 0.2500 24.7500 164.435425 27 16.5000 0.2500 24.7500 164.435426 27 16.5000 0.2500 24.7500 164.435428 29 18.0000 0.2500 27.0000 179.384128 30 18.0000 0.2500 27.0000 179.384128 31 18.0000 0.2500 27.0000 179.384129 30 18.0000 0.2500 27.0000 179.384129 31 18.0000 0.2500 27.0000 179.384130 31 18.0000 0.2500 27.0000 179.3841

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