Marketing Letters 12:3, 211±223, 2001
#2001 Kluwer Academic Publishers. Manufactured in The Netherlands.
Talk of the Network: A Complex Systems Look at the
Underlying Process of Word-of-Mouth
School of Business Administration, The Hebrew University of Jerusalem, Jersalem, Israel 91905
Davidson Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology,
Haifa, Israel 32000
Leon Recanati Graduate School of Business Administration, Tel Aviv University, Tel Aviv, Israel 69978.
*Corresponding author: e-mail: email@example.com
Received November 2000; Revised February 2001; Accepted February 2001
Though word-of-mouth (w-o-m) communications is a pervasive and intriguing phenomenon, little is known on its
underlying process of personal communications. Moreover as marketers are getting more interested in harnessing
the power of w-o-m, for e-business and other net related activities, the effects of the different communications
types on macro level marketing is becoming critical. In particular we are interested in the breakdown of the
personal communication between closer and stronger communications that are within an individual's own
personal group (strong ties) and weaker and less personal communications that an individual makes with a wide
set of other acquaintances and colleagues (weak ties).
We use a technique borrowed from Complex Systems Analysis called stochastic cellular automata in order to
generate data and analyze the results so that answers to our main research issues could be ascertained. The
following summarizes the impact of strong and weak ties on the speed of acceptance of a new product:
The in¯uence of weak ties is at least as strong as the in¯uence of strong ties. Despite the relative inferiority of
the weak tie parameter in the model's assumptions, their effect approximates or exceeds that of strong ties, in
all stages of the product life cycle.
External marketing efforts (e.g., advertising) are effective. However, beyond a relatively early stage of the
growth cycle of the new product, their ef®cacy quickly diminishes and strong and weak ties become the main
forces propelling growth. The results clearly indicate that information dissemination is dominated by both
weak and strong w-o-m, rather than by advertising.
The effect of strong ties diminishes as personal network size decreases. Market attributes were also found to
mediate the effects of weak and strong ties. When personal networks are small, weak ties were found to have a
stronger impact on information dissemination than strong ties.
Key words: word-of-mouth, social networks, cellular automata, complex systems
Word-of-Mouth (w-o-m) communications is a pervasive and intriguing phenomenon. It
has been generally found that both satis®ed and dissatis®ed consumers tend to spread
positive and negative w-o-m, respectively, regarding products and services which they
purchase and use (Anderson 1998). The signi®cant role of w-o-m in the dissemination of
market information is supported by broad agreement among practitioners and academics.
A long list of academic scholarship, industry market research and anecdotal evidence
points to the signi®cant affect of w-o-m on consumer behavior and, consequently, on
sales (e.g., Eliashberg, Jonker, Sawhney and Wierenga 2000; Krider and Weinberg 1998;
Buttle 1998; Dabaher and Rust 1996; Reichheld 1996; Herr, Kardes and Kim 1991;
Mahajan, Muller and Kerin 1984). Evidence also indicates that consumers' decision
making is strongly in¯uenced by w-o-m. Over 40% of all Americans actively seek the
advice of family and friends when shopping for services such as doctors, lawyers and
auto mechanics (Walker 1995). W-o-m has also been found to constitute a major input to
the deliberations of potential consumers regarding the purchase of new products (Rogers
Recognition of the signi®cance of w-o-m, coupled with growing reservations regarding
the effectiveness of commonly used forms of marketing communications, such as
advertising (Rust and Varki 1996), may explain the repeated calls in the business press
for managers to attend to the power of w-o-m (Wilson 1994; Grif®n 1995; Silverman
1997). Today's managers are diverting increased efforts to the management of w-o-m.
Recent anecdotal evidence con®rms an upward trend in the use of referral reward
programs, in which customers are compensated for ``spreading the word'' about a product,
and inducing product consumption by their acquaintances (Biyalagorsky, Gerstner and
Libai 2001). Diverse marketers, including museums (DeMasters 2000), book publishers
(Cohen 1999) and movie producers (McCarthy 1999) have launched w-o-m campaigns
with reported success.
Furthermore, the mounting use of the Internet, enabling surfers to communicate quickly
with relative ease, has established the contemporary version of this phenomenon, known as
``Internet w-o-m'' or ``word of mouse'', as an important marketing communication
channel. In what is sometimes labeled as ``viral marketing'', companies are currently
investing considerable efforts to trigger a word of mouse process and accelerate its
distribution (Schwartz 1998; Oberndorf 2000).
However, the current interest in w-o-m management has yet to succeed in transforming
managers' entrenched perceptions of the w-o-m phenomenon as a ``black box''. Main-
taining explicit or implicit beliefs that the personal in¯uence process is beyond their
control (Silverman 1997), managers hope, at the most, to ``manage'' rather than ``direct''
w-o-m effects. Unfortunately, as most academic research and writing on w-o-m in areas
such as marketing or communications has concentrated on the individual or personal
network level (e.g., Herr, Kardes, and Kim 1991; Gilly, et al. 1998; Brown and Reingen
1987), academic marketing research offers little to mitigate managers' sense of inef®cacy.
Unlike other areas of marketing communications, such as advertising, sales promotion or
sales force (e.g., Boulding, Lee and Staelin 1994; Jeddidi, Mela and Gupta 1999), in which
signi®cant attention has been given to assessing aggregate effects on sales, little is known
about how w-o-m aggregates to impact sales levels.
One cause of this gap in knowledge relates to the underlying complexity of the w-o-m
process. The spread of information in a given social system may be described as ``an
adaptive complex system'', i.e., a system that consists of a large number of individual
212 GOLDENBERG ET AL.
entities which interact with each other (in what is sometimes an indiscernible manner),
ultimately generating large-scale, collective visible behavior. Although the individual
interactions may be simple in many such adaptive systems, the large scale of the system
at work allows the emergence of patterns which are hard to predict, hard to track
empirically, and are often almost impossible to analyze analytically (Waldorp, 1992).
Various disciplines, such as physics, biology and ecology, have developed theories and
methods to investigate the evolution of complex systems. In the social sciences, which
recognize the inherent complexity of many social systems such as markets and organiza-
tions, attention has recently been drawn to the analysis of complex systems, speci®cally in
the ®elds of economic analysis (see Rosser 1999) and organizational management (e.g.,
Anderson 1999). However, this trend is still in its infancy, and research activity has yet to
invest in the question of how micro-level w-o-m activity governs macro-level effects.
Here, we offer a technique for linking w-o-m micro- and macro-phenomena, employing
stochastic cellular automata, a tool for complex system analysis. Cellular automata models
are simulations of aggregate consequences, based on local interactions between individual
members of a population. In the case of w-o-m, these local interactions are diverse types of
interpersonal interactions. In the speci®c model presented here, we concentrate on the
emergence of macro-effects from micro-effects, based on one of the fundamental theories
of communications, known as the ``strength of weak ties'' (Granovetter 1973).
1. Weak and Strong Ties
The theory of ``the strength of weak ties'' (Granovetter 1973) offers one of the most
important conceptual explanations of the process by which micro-level interactions affect
macro-level phenomena. Granovetter claimed that individuals are often in¯uenced by
others with whom they have tenuous or even random relationships. These in¯uences are
labeled ``weak ties'', to distinguish them from the more stable, frequent and intimate
``strong tie'' interactions that characterize individuals' personal networks. Although
weaker in absolute impact on the individual level, the signi®cance of weak ties lies in
their potential to unlock and expose interpersonal networks to external in¯uences
(individuals in distant networks), thus paving the path for the spread of information
Since its publication, Granovetter's theory has been the object of repeated inquiry, albeit
primarily in contexts not directly related to marketing research, such as job searches or
migration patterns (e.g., Bian, 1997; Wilson, 1998). Adopting a consumer research
orientation, Brown and Reingen (1987) generally found support for the focus on the
two types of w-o-m ties proposed by Granovetter. They found that although strong ties
were more likely to be activated and perceived as in¯uential in consumers' decisions, weak
ties were more likely than strong ties to facilitate w-o-m referral ¯ows. Duhan et al. (1997)
also found support for these two distinct paths of in¯uence, noting that factors such as
consumers' previous knowledge or perceived task dif®culty affect consumers' information
reception from different sources. Other empirical work found that when ties are strong,
w-o-m receivers are more likely to actively look for information and that the w-o-m
TALK OF THE NETWORK 213
information will have a signi®cant in¯uence on the receiver's purchase decision (Bansal
and Voyer 2000). However, Rogers (1995) suggests that even given the stronger informa-
tion ¯ow within strong ties, weak ties play a crucial role in the spread of information by
word-of-mouth on the aggregate level, especially about innovations.
While it is clear that weak and strong ties may be conceptualized as two distinct paths of
information dissemination, we know little about their macro-effects. For example, we lack
any comparative data on the respective rates of dissemination of these two mechanisms,
nor do we know how they interact with other marketing efforts such as advertising. Given
the increased efforts to ``manage'' w-o-m, improving our understanding of how these two
major paths of w-o-m affect information dissemination should be of great interest to
In our present study, we employ stochastic cellular automata to investigate the following
1. Which of the effects - strong ties, weak ties or marketing efforts - has more in¯uence on
the aggregate growth of information dissemination?
On the one hand, information is expected to pass more readily through strong ties, due
to their larger frequency of activation and perceived reliability. However, weak ties are
essential for initializing the information ¯ows in distinct networks. What is the time-
dependent relationship between these two forces?
2. How do personal network size and quantity of weak ties affect the in¯uence of strong
and weak ties on the aggregate growth of information dissemination?
How do factors such as the number of weak ties contacts and network size (number of
individuals in a typical personal network) mediate the consequential effects of weak and
3. How does advertising interact with strong or weak ties to affect the aggregate growth
of information dissemination?
Which of the two types of w-o-m paths will be more highly impacted by the presence of
marketing support such as advertising?
2. Cellular Automata
Cellular automata is a complex systems modeling technique, which simulates aggregate
consequences based on local interactions between individual members of a population.
Individual members in the model may represent plants and animals in ecosystems, vehicles
in traf®c, people in crowds or autonomous units in a physical system. The models typically
consist of a framework in which interactions occur between various types of individuals. In
stochastic cellular automata model, each individual's behavior is dictated by a prede®ned
scheme of response probabilities and is a function of the state of other individuals with
whom he interacts (see, for example, Holland 1995). The solution of such models consists
of tracking the changing state of each individual over time. Thus, cellular automata is
distinct from alternative modeling techniques that use individual attributes to calculate
214 GOLDENBERG ET AL.
average population attributes and then simulate changes in the ``average'' population. For
recent applications of complex systems models to marketing problems see Krider and
Weinberg (1997), Goldenberg et al. (2000) and Goldenberg, Libai and Muller (2001).
Figure 1 depicts the cellular automata model graphically. The model consists of a ®nite
number of virtual individuals in a given simulated social system, each of whom is able to
receive information during consecutive, discrete periods. Social interactions in the system
are of two types: proximal contacts among members of the same network and weak ties
interactions with individuals belonging to different networks. We de®ne two states
of individuals: ``informed'' ± those who have received the relevant information and are
informed of the phenomenon ± and ``uninformed'' ± those individuals who have not
received the information. The model makes use of the following additional assumptions:
1. Interpersonal contacts (b) are de®ned as the probability of an uninformed individual to
be affected by an informed individual, in one period, i.e., change his=her state from
``uninformed'' to ``informed''. Subscripts sand w, respectively, differentiate interactions
in which the source of the information belongs to the individual's network or to a
different network. Re¯ecting theory and previous research (e.g., Brown and Reingen
is larger than b
. Thus, the probability of an individual to be affected by other
individuals in his own network is greater than the probability of changing his state from
uninformed to informed as a result of contacts with other, weak ties individuals.
2. Each individual ``belongs'' to a single personal network. Each network consists of
individuals who are connected by strong ties (b
). In each period, individuals also
conduct a ®nite number of weak ties interactions with individuals outside their personal
networks ( b
Figure 1. Market with Personal Networks. Strong Ties (bs) are Depicted with Solid Lines while Weak Ties (bw)
are Depicted with Dotted Lines.
TALK OF THE NETWORK 215
3. Uninformed individuals also have a one period probability, a, of becoming informed
through their exposure to other marketing efforts, such as advertising. Following the
w-o-m literature (e.g., Buttle, 1998), the probability of being affected by advertising
exposure is assumed to be smaller than the effect of a w-o-m contact. Although the
present model incorporates advertising, other mass media sources of marketing
information are hypothesized to have a similar effect.
In the ®rst stage of the analysis, we de®ne the range of the individual level parameters to be
analyzed by a computer program (written in C for this study). The program both generates
individual level data and aggregates these results to plot macro-level adoption curves. In the
second stage of analysis, individual level and aggregate level data are fed into a statistical
program (SAS) to perform the necessary statistical analyses to identify main effects.
We divide the entire market equally into personal networks, in which each individual
can belong to one network. In addition, in each period every individual conducts random
meetings with other individuals external to his personal network.
Thus if in period t, an individual is connected to minformed others belonging to his or
her personal network and jinformed others who are random contacts represented by weak
ties, the probability of the individual becoming informed in period t, is given by:
The following step-by-step outline describes the cellular automata algorithm:
Period 0: This is the initial condition where all individuals are uninformed (receiving the
value of 0)
Period 1: The probabilities for each individual (given by equation 1) are realized. Clearly
only advertising is at work in this period as word-of-mouth needs informed
individuals to start the process. A random number U is drawn from a uniform
distribution in the range [0,1]. If U <p(t) then the individual moves from non-
informed to informed (receiving the value of 1). The individual stays non-
Period 2: The informed individuals begin the w-o-m process by deploying their strong
ties within their own personal network, and weak ties to other networks.
Probabilities are realized as in step 1, and the random number is drawn so that
when U <p(t) the individual moves from non-informed to informed.
Period n: This process is repeated until 95% of the total market (3000 individuals)
All combinations of the parameters were considered in a full factorial design experiment.
Each of the ®ve input variable parameter s was manipulated on seven levels, to produce overall
216 GOLDENBERG ET AL.
16,808 information dissemination process simulations. Each process was terminated
when 95% of the population attained informed status. Parameter ranges were set as follows:
1. Size of each individual's personal network 5±29
2. Number of each individual's weak ties contacts 5±29
3. Effect of weak ties (b
4. Effect of strong ties (b
5. Effect of advertising (a) 0.0005±0.01
Note that since weak and strong ties effects represent probabilities, their absolute value
range determines the magnitude of a ``period'', which is less of an interest to us. Our interest
lies with the relative values of the parameters analyzed. Consistent with previous literature
as speci®ed above, we set the advertising effect to be in a range that is lower than the range
of the w-o-m effects. In addition, the weak ties probabilities are set to be lower than the
strong ties probabilities. Networks size range were set to re¯ect a reasonable range of
personal contacts, and while the ranges of weak ties and strong ties contacts are the same,
through the simulation we can analyze the effect of different combinations of their sizes.
After generating all possible outcomes of the above manipulations, a number of analyses
were conducted to explore the relationship between weak and strong ties and the rate of
information dissemination. One possible aggregate level measure, All Informed, is the
number of periods elapsing before 95% of the population becomes informed. However,
cellular automata modeling enables us to extend our examination and discover more
complex, perhaps non-linear, effects, by observing the succession of changes occurring
over the life-span of the process. More speci®cally, to understand how the respectiveimpacts,
weak and strong ties, evolve over the different stages of the process, we look at Early
Informed, Middle Informed and Late Informed - variables re¯ecting the number of periods
elapsing before 0±16%, 16±50 % and 50±95% of the market become informed. We denote
the time from the onset of the process until 16% of the market has attained ``informed''status
and so forth. Three OLS regressions, designed to relate aggregate level measures
to micro-level parameter values, were conducted, with Early Informed, Middle Informed and
Late Informed respectively as the dependent variables, and the network and in¯uence
parameters outlined above as the dependent variables. Regression results presenting the
effects of the different communication parameters are given in Table 1. We also examined the
impact of the interactions between the size of personal networks, the number of weak ties and
advertising, on the one hand, and weak and strong ties on the other. This was done by running
an OLS regression for each factor value and the other four parameters as independent
variables, with All Informed as the dependent variable. Results are given in Figures 2±4.
The following main results raised some interesting observations:
Result 1: The in¯uence of weak ties on the speed of information dissemination is at
least as strong as the in¯uence of strong ties.
TALK OF THE NETWORK 217
Despite the relative inferiority of the weak tie parameter in the model's assumptions
(strong ties re¯ect a greater probability for an individual-level transformation), their effect
approximates or exceeds that of strong ties, in all three process stages (see Table 1). These
results challenge the emphasis placed, in most of the research on w-o-m, on strong ties
as the important means of information dissemination (Brown and Reingen, 1987) and
provide quantitative support for Granovetter's theory (1973) in this regard. However,
recalling our conceptualization of the market as a complex system, these results should not
cause us excessive surprise. Like most complex systems, interactions and non-linear
effects may be present beneath the surface.
While this ®nding is intriguing at all stages of the information growth process, the
increasing importance of the effect of weak ties during the middle stage (T
suggests that their signi®cance stems from their unique effect on growth, rather than from
their prevalence. De®ne ``activated networks'' as networks containing at least one informed
individual. Closely tracking the dynamics of the process reveals that the initially large
proportion of uninformed individuals in activated networks gradually decreases as more
individuals become informed in each network. Since the impact of strong ties is related to
the ratio of uninformed to informed individuals in each network, as more individuals
become informed, the potential effect of strong ties is gradually exhausted. When all
members of activated networks become informed, the effect of strong ties is contingent
upon on the activation of new networks, a task performed by the weak ties. The increasing
slope of the effect of the weak ties between the ®rst and middle stages thus re¯ects the fact
that the successive activation of new networks through weak ties enables the continuation
of the process.
Result 2: Beyond a relatively early stage of the process, the effect of external marketing
efforts (e.g., advertising) quickly diminishes and strong and weak ties become
the main forces propelling the process.
The results clearly indicate that information dissemination is dominated by both w-o-m
paths, rather than by advertising. This con®rms ®ndings from the diffusion of innovation
literature, which pointed to w-o-m as the main factor driving the speed of innovation
diffusion (Rogers 1995; Mahajan, Muller and Srivastava 1990).
Moreover, the results in Table 1 also provide quantitative support for Rogers' (1995)
argument that, while advertising may be important in the initial stages of information
Tab le 1. A Comparison of the Effects of Weak and Strong Ties on the Speed of Information Dissemination (The
Dependent Variable is the Number of Periods Comprising Each Process Stage, the OLS Parameters are
Strong ties effect 70.25 70.33 70.37
Weak ties effect 70.26 70.40 70.38
Advertising effect 70.61 70.11 70.04
0.66 0.60 0.63
All variables are signi®cant at p 0.0001 level.
218 GOLDENBERG ET AL.
dissemination, the main mechanism driving innovation diffusion after product takeoff is
Our ®ndings show how the major role of marketing efforts in the initial stage of the
process (their impact is twice as powerful as that of either the strong or weak ties)
diminishes after 16% of the market becomes informed. When information dissemination
reaches the halfway mark (i.e., 50% of all individuals are informed), the impact of
marketing efforts diminishes further, to one-third and one-quarter of the impact of strong
ties and weak ties, respectively. Although in the initial stage, strong and weak tie effects
were almost equal in potency, weak ties have a larger effect than strong ties, relative to the
advertising effect, in the second stage of the process.
Result 3: The effect of strong ties on the speed of information dissemination diminishes
as personal network size decreases.
Market attributes were also found to mediate the effects of weak and strong ties, as this
and the following results show. When personal networks are small, weak ties were found to
have a stronger impact on information dissemination than strong ties. A non-linear
relationship between weak ties and network size was indicated (see Figure 2).
Result 4: As the number of weak ties contacts increases, the effect of strong ties
decreases while the effect of weak ties increases (see Figure 3).
Result 5: As the level of advertising increases, the effects of both strong and weak ties
are marginally impacted, in inverse directions: the effect of strong ties
increases while the effect of weak ties decreases (see Figure 4).
Figure 2. The Effects of Strong and Weak Ties on Speed of Information Dissemination as a Function of Personal
TALK OF THE NETWORK 219
5. Discussion and Implications
In the present study, we demonstrated how complex systems analysis (stochastic cellular
automata in our case) contributes to our understanding of the aggregate level effect of
Figure 3. The Effects of Strong and Weak Ties on Speed of Information Dissemination as a Function of the
Number of Weak Ties Contacts.
Figure 4. The Effects of Strong and Weak Ties on the Speed of Information Dissemination as a Function of
220 GOLDENBERG ET AL.
weak and strong social ties, in terms of the spread of information through word-of-mouth.
First, as Table 1 demonstrates, for the range of parameters examined here, weak ties have
an in¯uence on information dissemination, which is at least equal to that of strong ties.
Second, both types of social effects have a stronger in¯uence on information dissemination
than the effect of advertising.
As shown in Figures 2±4, the relative effects of strong and weak ties may depend on
other factors, such as personal network size, number of weak ties interpersonal interactions
characterizing a social system, and advertising. When network size is small, or weak ties
contacts are numerous, or advertising effect is weak, weak ties may have a greater impact
on the rate of information dissemination than strong ties.
These results have important managerial implications. Managers attempting to in¯uence
w-o-m spread should distinguish between the two kinds of social interactions that
contribute to both positive and negative w-o-m communications. For example, in certain
situations managers may want to distinguish referral rewards for referrals of close friends
and family members from rewards for referring others. When personal networks are large,
weak ties contacts among inter-network individuals are few, or the advertising effect is
strong, fostering inter-network ties may be one of the few options available to marketers.
Moreover, as ®ndings from the diffusion of innovations literature suggest, w-o-m and
advertising effects may differ among different market segments (Rogers and Kincaid,
1981; Rogers, 1995). Marketers are advised to develop market research, which would
provide estimates of these factors for different segments and products.
While this study adds to our knowledge by exploring the aggregate level effect of weak
and strong w-o-m ties, we recognize its limited scope, especially considering the wide
range of analyses enabled by cellular automata methods for the exploration of phenomena
such as w-o-m. This technique, due to its unique features and especially the ability to
model a wide variety of market situations, is suited to model many marketing phenomena
that have been traditionally under-researched. We believe it is especially suited to analyze
interpersonal based processes such as the growth of new products and other w-o-m based
social phenomena that have been only partially explored due to the complexity inherent in
these processes. Where diffusion of innovations modelers are often restricted by simplify-
ing assumptions, cellular automata enables us to deeply explore real life phenomena that
are not analytically tractable. It is especially suited to model individual level heterogeneous
behavior where the aggregation is done by the program itself without having to resort to
simplifying assumptions needed for the aggregation.
For example, such methods may be used to explore web-based information dissemina-
tion or the consequences of diverse ``viral marketing'' approaches using w-o-m channels
such as ``chat rooms'', websites of various sizes containing links to other sites, large-scale
information transmission though e-mail lists and web-based referral reward programs.
Other non-web examples include an analysis of time-based changes of marketing mix and
consumer behavior variables for new product growth (e.g., price, advertising, repeat
purchase, market potential), the optimal marketing in the presence of network externalities
or the optimal marketing to early and mainstream markets for high-tech products.
Considering the options complex system methods such as cellular automata open for
researchers, it is clear that this is just a short list for promising future research.
TALK OF THE NETWORK 221
The authors would like to thank Moshe Givon, John Hogan, David Mazursky, Charles
Weinberg and two anonymous reviewers for their insightful comments and suggestions.
This research was supported by The Israel Science Foundation founded by the Israel
Academy of Sciences and Humanities and by grants from the K-mart International Center
of Marketing and Retailing, and Davidson Center at the Hebrew University and the Israeli
Institute for Business Research ar Tel Aviv University.
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