ORIGINAL ARTICLE

A trust-based multi-ego social network model to investigateemotion diffusion

Di Wang • Alistair Sutcliffe • Xiao-Jun Zeng

Received: 30 September 2010 / Revised: 23 January 2011 / Accepted: 5 February 2011 / Published online: 11 March 2011

� Springer-Verlag 2011

Abstract In this paper, we propose a computational

model: trust-based multi-ego social network to investigate

and understand dynamic emotion diffusion through the

whole population and the result of this dynamic diffusion.

The key advantage of our proposed computational model is

that it is able to answer the questions of ‘why’ some indi-

viduals are happier than others and ‘what…if’ question (e.g.

what happens if we increase social behaviours in a hard

period, such as economic crisis) by changing the parameter

setting for the model. From the simulation results, we show

that, first emotion diffusion and social support help in

increasing the happiness for both individual level and the

whole society level; secondly, individuals with high hap-

piness factor (high happiness genes) and more friends

(hence more social support) tend to be happier.

Keywords Social network � Happiness � Social support �Happiness diffusion � Emotion diffusion � Wellbeing

1 Introduction

Happiness is the most fundamental object of our life and

the secret motive for what we are doing (William 1902).

Much research has been done in the recent 40 years

investigating the elements that stimulate the happiness of

human beings, including economics (Easterlin 1974;

Alberto et al. 2004; Ulf-G and Magnus 2001; Alois 2004;

Rafael and Robert 2006; Rafael et al. 2003; Rafael et al.

2001; Bruno and Alois 2002) (specially income(Gardner

and Oswald 2007; Kahneman et al. 1908; Clark and Oswald

1996) and welfare (Ng 1978), lifecycle (Richard 2006;

Richard 2001), illness and health (Ulf and Magnus 2001;

Ubel et al. 2003; Lisa 1984), pollution (Heinz 2006),

political policy (Bruno and Alois 2000; Csikszentmihaly

1991), neuroscience (Csikszentmihaly 1991; Wilson et al.

2003), evolutionary biology (Gervais and Wilson 2005),

lottery (Gardner and Oswald 2007), job (Clark and Oswald

1994; Andrew 1997), socioeconomic (Subramanian et al.

2005), inequality (Graham and Felton 2006), divorce (Zivin

and Christakis 2007), bereavement (Zivin and Christakis

2007), genes (Ubel et al. 2003), and social behaviors

(William 1902).

Researchers first argued that there was a link between

happiness and economics, i.e. financial status, money,

income and inflation. Richard Easterlin (1974) was one of

the first economists to investigate economic statistics on

happiness level over time. It was guessed that, first, with

the development of economics and living standard over

time, the individual happiness level for the whole popula-

tion was expected to increase; and secondly, people in rich

countries were expected to be happier than people in poor

countries. However, Richard Easterlin’s result goes to the

other way. His result shows, first, individual happiness

appears to be the same across poor countries and rich

countries, and, secondly, economic growth does not raise

well being. In another sentence, maximizing the economics

utility does mean maximizing the happiness (Richard

1995). Similar conclusion was drawn by Peggy Schyns

D. Wang (&) � A. Sutcliffe

Manchester Business School, University of Manchester,

Oxford Road, Manchester M15 6PB, UK

e-mail: di.wang@mbs.ac.uk

A. Sutcliffe

e-mail: a.g.sutcliffe@manchester.ac.uk

X.-J. Zeng

School of Computer Science, University of Manchester,

Oxford Road, Manchester M13 9PL, UK

e-mail: x.zeng@manchester.ac.uk

123

Soc. Netw. Anal. Min. (2011) 1:287–299

DOI 10.1007/s13278-011-0019-7

(1998): people in different countries with different GDP

have similar happiness level; however differences in hap-

piness appear across countries with different cultures. So

happiness level does not increase directly according to the

increase in economic utility given that the income arrives

at some basic level.

Then, Easterlin suggested that we should think of people

as getting the utility from a comparison of themselves with

others close to them. Comparison theory developed by Van

Prag and Kapteyn (1973), Easterlin (1974), and Brickman

et al. (1978) explains the reason as: human happiness

depends on comparisons between standards of quality of

life and perceived life circumstances. Comparison theory

states that happiness is relative: the increase in happiness

that one might have expected based on the growth in

individual incomes is offset by the decrease in happiness

due to the rise in the average, not the net growth in well

being. For example, Andrew J. Oswald (Andrew and Ana

2009) did the research on how much some internal and

external events influence the happiness level in quantity by

monetary valuation. They found that although the overall

happiness level is changed by some nationalized events,

such as inflation and jobless, the unhappiness from job-

lessness is easier to bear if a jobless person is surrounded

by jobless people in an area. This is an indication that both

positive and negative events might have different influence

on individual’s happiness level when the events are put into

some specific social network. This happiness comparison

theory indicates that happiness decided not only by one

individual, but also influenced by others surrounding and

elated to him/her. This is the main motivation of our

research: putting individuals in social network to investi-

gate happiness influence from others.

Happiness research also shows another psychological

factor that affects subjective evaluations of well-being,

which explains individuals’ ability to adapt to tremendous

positive or negative shocks and often even to return to

previous levels of happiness, which is called adaptation

theory (Richard 1995; Carol 2005; Carol and Stefano

2001). People adjust the objective and subjective life

through time based on what happen to them. In the short

run, their tremendous positive or negative shocks are

softened by a contrast effect, which enhances the bothers/

pleasures of ordinary things. In this sense, happiness level

can be considered as combination of emotions, which

eclipse over time. In our research, we consider emotions as

energy, which eclipse through time.

Therefore, the conclusion is that basic economic con-

dition is a prerequisite for happiness, however, it is not the

main element to determine happiness if it goes over some

baseline. If the basic needs are fairly gratified, there will

emerge other needs, such as love, affection, support and

belongingness, which become more important elements to

determine happiness level. For example, it has reported

(Bruno and Alois 2005) that married people are happier

than singles. However, we have not drawn a conclusion

yet whether marriage itself bring happiness to people or

happy people are more likely to get married. However,

there is a quite possible guess, that not only marriage itself

but also strong support from and happiness sharing

between partners is a source of happiness, and an adult is

able to get strong supports from their partner easily and

directly. As stated by Richard Layard (2006), once an

individual rises above a poverty line or ‘subsistence level’,

the main source of increased happiness is not income but

rather friends and a good family life and social behaviour

(support, networking and so on). To partly filter eco-

nomics and job pressure elements and investigate the

influence of social network on happiness, research for

social support were done for aging people. As an example,

research by Chan and Rance (2006) indicates that older

persons with a larger social network and more support are

happier and social support plays a mediating role from for

happiness.

All studies indicate that social network plays an

important role in determining individual happiness level.

We use the term of ‘happiness’ when we discuss related

work for consistency (they used ‘happiness’ in their work).

However, when we talk about ‘happiness’, we cannot

ignore its opposite elements: bother, worriment, sore or

fear, etc. In our work, we use the term of ‘emotion’ which

can be either positive or negative; we define ‘happiness’ as

positive emotion and its opposite (bother, worriment, sore

or fear, etc.) as negative emotion. We use the term of

‘happiness level’ when we talk about the accumulation of

all (positive and negative) emotions for an individual. In

our research, we proposed a computational model: trust-

based multi-ego social network which is a multiple agency

technique to investigate and understand the process of

emotion diffusion through social network and its result on

the happiness level for individuals and the whole society.

The key advantage of our proposed computational model is

that it is able to answer two types of questions: first,

through the result analysis, we can answer ‘why’ question:

why some individuals are happier than the others. Sec-

ondly, we can answer ‘what…if’ question by changing the

parameters for the model. These answers help us with a

direction to make policies and take actions to improve the

happiness level of the whole society.

In the Sect. 2, we introduce the idea of emotion diffu-

sion through social network. Section 3 describes our pro-

posed computational model: rust-based multi-ego social

network in detail. In Sect. 4, parameters for trust-based

multi-ego social network are explained. In Sects. 5 and 6,

we present the simulation results and analysis. In Sect. 7

some conclusions and discussions are given.

288 D. Wang et al.

123

2 Our research: investigating dynamic happiness

change for both individuals and group of individuals

using multi-ego network

All studies discussed above focus on the statistic analysis

for happiness related to other elements; however, have

not covered a possible key element to determine human

happiness: emotion diffusion (which is called as emotion

contagion or happiness contagion by some researchers)

between indivisibles. As mentioned in the above discus-

sion, we have seen strong indication that social support is a

most important element to determine happiness (e.g. old

people with more social behaviour are happier (Chan and

Rance 2006); married people are happier than singles

(Bruno and Alois 2005); employed people are happier than

unemployed people (Andrew 1997). Hence, social network

could be a method to investigate dynamic happiness not

only for individuals but also for group of individuals with

ties among them (Alvin 2011; John 2011; Frederic et al.

2011; Ilham et al. 2011; Muhaimenul 2011). Mitchell

(1969) defines a social network as ‘a specific set of link-

ages among a defined set of persons, with the property that

the characteristics of these linkages as a whole may be used

to interpret the social behavior of the persons involved’.

More simply, Bott (1971) defines a network as ‘all or some

of the social units (individuals or groups) with whom a

particular individual or group is in contact’. Social network

model was used as a potentially theoretical model to

describe and analyze social systems, study the interactions

and support between individuals, in terms of the whole

system rather than an individualistic approach (Christopher

1976). The structural form of a social network determines

the flow of emotion diffusion through specific ties. Fowler

and Christakis (Fowler and Christakis 2009) investigate

whether happiness in an ‘ego’ (a key person in the study) is

affected by the happiness of ‘alters’ (people connected to

the ego). The work by Fowler and Christakis (2009) posit

the hypothesis that some psychosocial determinants could

be transmitted through social connections. However, more

work is needed to verify the presence and strength of this

diffusion, and to identify the specific processes. Currently,

how emotions diffuse among the social network and how

the social behaviours and social support change individual’s

happiness level is unknown. Our research will fill this gap.

When we talk about ‘‘happiness’’, we can not ignore its

opposite elements: bother, worriment, sore or fear, etc. If

we call all these elements including happiness as emotion,

we could have positive emotion such as happiness and

negative emotion such as bother, worriment, sore or fear,

etc. These emotions (either positive or negative) can spread

in the social network (Fowler and Christakis 2009) in

different degree and change the happiness level of the

involved individuals, which is called emotion diffusion.

Sometime emotion diffusion can get feedback which is

called as emotion resonance (similar with energy reso-

nance). We could reasonably say that, emotion is a kind of

energy which can be generated by events from outside

world or from human being’s inside mysterious mechanism

(Rafael et al. 2003; Andrew and Ana 2009), diffuse (Lisa

1984) and resonance among social network in some degree

and be shorten by contracting effect through time (Richard

1995; Carol 2005; Carol and Stefano 2001). In another

sentence, individual’s happiness level is not merely a result

of personal character and experience, but also is a result of

groups. Emotions are a collective phenomenon. However,

how emotions diffuse in a social network from person to

person and influence the happiness level of individuals in

the whole group or even the whole society is unknown. In

our research, we investigate how emotions diffuse through

social network and change the happiness level of an indi-

vidual and a group of individuals by using trust-based

multi-ego social network model.

In summary, pervious studies are focused on the statistic

relationship between happiness level and relevant elements,

such as economics, policy, and social support, etc.

Although their results give a hint that social activity and

social support play a very important role to happiness, how

social behaviour change happiness level is unknown. In

addition, they ignore the differences between individuals

(such as the personal characters and backgrounds) and

dynamic happiness level changes through emotion diffu-

sion for these different individuals. Individuals with

different personal characters and moods might react com-

pletely different to the same event, social activity and social

support. In another sentence, similar events (such as policy,

economics and events) have different results to individuals

with different personal characters and backgrounds. This

applies to the influence of social behaviour and support as

well. Individuals with different personal characters and

backgrounds might have different reflection to social

behaviour and support.

Happiness level for a group is a collective phenomenon

of all events happening to all individuals. Our research

focuses on the dynamic interactions (social behaviour)

between individuals and the consequence of these inter-

actions to different individuals and to the whole group. We

construct a computational model to investigate the emotion

diffusion among social network and the results on happi-

ness level for individuals and the whole group. We use

multiple agent technique to model the whole society, with

each agent representing an individual who has its own

personal character and background. In the following dis-

cussion, we use the term of ‘ego’ to represent an agent or

individual in the social network. In our research, we con-

sider an emotion (either positive or negative) as an energy.

These emotions can be generated by events from either

A trust-based multi-ego social network model 289

123

outside or inside world and shorten by contracting effect

through time, diffuse (which is emotion diffusion) and

resonance among (which is emotion sharing) social net-

work in some degree in a period and as a consequence

change the happiness level of the involved individuals in

the social network. Negative emotions sometimes get

feedback as comfort (which is considered as a type of

social support), and as a result, the unhappiness of the ego

can be softened in some degree through this comfort.

Positive emotions sometimes get positive resonance (which

is emotion sharing and happiness resonance among family

and friends) in some degree. Social support is obtained by

emotion sharing among friends, emotion resonance

between friends, and emotion comfort from friends. Hence,

generally speaking, the more friends an individual has, the

more social support he/she can get.

3 Model description

Our research focuses on the dynamic interactions (emotion

diffusion) between individuals and the consequence of

these interactions to happiness level to different individuals

and the whole group. We use multiple agent technique to

model the whole society, with each ego representing one

individual who has its own personal character and back-

ground. In the following discussion, we use ‘ego’ to

represent an individual in the social network; we use

‘neighbours’ when we are talking about an ego’s family

members and close friends with strong trust. Emotion dif-

fusion algorithm based on the trust strength is implemented

between egos. Emotions diffuse and resonance through

network, and eclipse through time. Each individual is

connected to its neighbours through trust strength. Differ-

ent links have different trust strength. In the following

discussion, we use ‘focal ego’ when we talking about an

ego undergoing an event or broadcasting its emotion to its

neighbours; we use ‘alter ego’ when we are talking about

an ego accepting emotion from the focal ego. Trust is an

underlying rule determining how much a focal ego’s

emotion influences the alter ego. The stronger the trust, the

more influence the alter ego gets.

In the experiments, we are use 200 iterations/turns (in

the following we use term ‘turn’). In each turn, each ego

has its opportunity to both come across outside event

(either positive or negative) and diffuse its emotion to its

neighbours. Emotion diffusion happens only from the focal

ego to its direct neighbours (one-step-diffusion) in each

turn. Emotion diffusion means that the focal ego sends its

latest event it comes across or news it just heard to its

neighbours. Through this emotion diffusion, the focal ego

shares its happiness and confides its bother with others and

gets support from them.

Then, we test a larger size population with a general ad

hoc network structure. We set 200 egos in the social net-

work, which is generated by simulating Dunbar’s Social

Brain Hypothesis (SBH) (Dunbar 1996, 1998). In SBH, an

individual has roughly 150 people in his/her social memory

or within his/her social range. So a population of 200 is

able to give a reasonable simulation result for emotion

diffusion which leads to a general conclusion. SBH posits

that individual social networks are structured into a hier-

archically organised series of sub-groupings that exhibit

different levels of intimacy (Zhou et al. 2005). SBH indi-

cates that people’s relationships (family, relatives and

friends) can be broken down to levels based on the trust

strength. When we are talking about our friends who share

our happiness and suffer, and give us support, they are the

ones with strong trust with us.

To make our conclusion more general, we also look into

a benchmark social network structure, small network in

Sect. 6 (Dunbar 1998).

4 Parameters and formulas description

In our experiment, eight parameters are involved: two

parameters for individuals to determine genes (personal

characters) and the background, and six social parameters

to determine the emotion diffusion mode. The two

parameters for individuals are different from individual to

individual, and the six social parameters are the same for

all individuals in each run.

4.1 Parameters for individuals:

Happiness factor: each individual has its own happiness

factor, which is determined by gene. It has been shown that

there is a strong relation between individual happiness

level and genes. People having happiness genes are easy to

be cheered up by small pieces of positive signals, vice

versa. In our experiment, happiness factor for each indi-

vidual is randomly generated (ranging from 0.5 to 1.5, and

1 is the normal happiness gene), in order that we can look

into how events (positive or negative) and emotion diffu-

sions influence the happiness level to different individuals

with different happiness factors. People with high happi-

ness factor are easy to be cheered up by positive signal,

meanwhile have positive attitude to negative signal and

easy to get through difficulties, vice versa.

Initial happiness level: in addition to the gene-

determined factor, different people have different back-

grounds. In our experiment, initial happiness level for each

individual is randomly generated (ranging from -0.5 to

0.5), in order that we can look into how events (positive or

negative) and emotion diffusions influence the happiness

290 D. Wang et al.

123

level to different people with different initial happiness

level (i.e. background).

Happiness factor is determined by genes and can not be

changed through an individual’s whole life. It determines

the attitude of an individual toward (positive/negative)

events happening to him/her and emotion diffusion influ-

ence from his/her to neighbours. Initial happiness level

determines the starting point of an individual’s happiness

level in our experiments and has no influence on happiness

changes through events (positive or negative) and emotion

diffusions. Using the parameters of happiness factor and

initial happiness level, we distinguish individuals by their

personal characters and their backgrounds. Individuals with

different personal characters react different to the same

event, social activity and social support.

4.2 Social parameters

In our research, we consider emotion (either positive or

negative) as energy. These emotions can be generated by

events, shorten by contracting, spread and resonance

among social network, and as a consequence change the

happiness level of involved individuals in the social

network. Negative emotions sometimes get feedback as

comfort, and as a result the unhappiness level can be

softened through this comfort. Positive emotions some-

times get positive resonance depending on the happiness

level of the alter ego. We will explain when comfort or

positive resonance happens in the next subsection. In our

research, we investigate the dynamic flows of emotions

through the social network and how these flows influence

the happiness level of both individuals and the whole

group. To do this, six parameters are used to control the

events happening and the emotion diffusions.

Event probability: this is the probability (from 0 to 1) of

event (either positive or negative) happening to the focal

ego in each turn. An event occurs at this probability to each

focal ego in each turn.

Emotion diffusion probability: this is the probability

(from 0 to 1) of the focal ego broadcasting its latest event/

information to its neighbours through trust-based links in

each turn.

Diffusion factor for positive emotion: this is the multi-

plier (from 0 to 1) to emotion energy when an alter ego

receives positive information from its neighbours. This

multiplier is between 0 and 1 which means that a friend or

a family member share part of the happiness from the focal

ego.

Diffusion factor for negative emotion: this is the multi-

plier (from 0 to 1) to emotion energy when an alter ego

receives negative information from its neighbours. This

multiplier is between 0 and 1 which means that a friend or

a family member share part of the unhappiness from the

focal ego.

We can set the same value to broadcasting factor for

both positive and negative emotions. These two broad-

casting factors work together to control the strength of

emotion diffusion. We are not clear whether positive and

negative information diffuse at the same rate or not. We set

them as two separate parameters for further parameter

sensitivity analysis.

Comfort factor: this is the multiplier (from 0 to 1)

showing how much the focal ego can be alleviated from

negative event/information from its neighbours’ support

after broadcasting its negative event/information to its

neighbours. This multiplier is between 0 and 1 which

means that negative emotion can only be partly comforted

by a friend or a family member.

Resonance factor: this is the multiplier (from 0 to 1)

indicating the additional happiness the focal ego gets by

sharing its positive events/information with its neighbours.

This multiplier is between 0 and 1 which means part extra

happiness increase by happiness resonance.

4.3 Equations to control event happening and emotion

diffusion through social network

In the following discussion, we use ego i to represent the

focal ego and ego j to represent the alter ego. At the

beginning, the happiness level for each ego is initialized

by its initial happiness level representing its background.

Then in each turn, an event occurs at a probability of

Event probability to each focal ego and emotion diffusion

from focal ego to its neighbours happens at a probability

of Emotion diffusion probability.

Each event happens with an initial energy and decay

rate. The values of initial energy (ranging from -1 to 1)

and decay rate (ranging from 0 to 1) for each event are

randomly generated on the fly. However, the same event

results in different emotion energy to different egos based

on their personal characters (i.e. happiness factor). This is

consistent with the literature.

Energyk;i0 ¼ Energy Inik � Happiness Factori ð1Þ

where i is identity of the focal ego, k is the identity of

emotion and Energy_Inik is the initial energy of this event,

Energy0k,i is the initial energy of emotion k for ego i.

The energies for all emotions are decaying at their own

decay rates through time. The energy decay function in

each turn is

Energyk;itþ1 ¼ Energyk;i

t � Decay Ratek ð2Þ

where k is the identity of emotion, Decay_Ratek is the

decay rate for emotion with identity k, Energytk,i is the

A trust-based multi-ego social network model 291

123

energy for this emotion at time t for ego i, and Energyt?1k,i is

the energy for this emotion at time t ? 1 for ego i.

At each turn, emotion diffuses from its focal ego to its

neighbours at a probability of Emotion diffusion proba-

bility. Assume emotion diffuses from ego i (the focal ego)

to ego j (the alter ego).

If Energytk,i is a new emotion to alter ego j (ego j has not

heard of the relevant news) and Energytk,i [ 0.

Energyk;jt ¼ Energyk;i

t � diffusion multiplier Pos

� trustij

average total trust� happiness factorj

ð3Þ

Else if Energytk,i is a new emotion to alter ego j (ego

j has not heard of the relevant news) and Energytk,i \ 0.

Energyk;jt ¼ Energyk;i

t � diffusion multiplier Neg

� trustij

average total trust� 1

happiness factorj

ð4Þ

where diffusion_multiplier_Pos and diffusion_multiplier_

Neg are multiplier for positive and negative emotion

respectively, which are ranging from 0 to 1, trustij is the

trust between ego i and ego j, happiness_factorj is

the happiness factor for the alter ego: ego j, and

average_total_trust is the average total trust of the whole

population, which is defined as:

average total trust ¼PN

i¼1

Pni

m¼1 trustijm

Nð5Þ

where N is the total number of egos, ni is the total neigh-

bours for ego i, jm is the identity of ego i’s neighbours.

Similarly, if Energytk,i is not a new emotion to ego j (ego

j has heard of the relevant news before) and Energytk,i [ 0,

then the new energy for the relevant news for ego j is:

Energyk;jt ¼Energyk;j

t þEnergyk;it

�diffusion multiplier Pos

� trustij

average total trust�happiness factorj ð6Þ

If Energytk,i is a not new emotion to ego j (ego j has

heard of the relevant news before) and Energytk,i \ 0, then

the new energy for the relevant news for ego j is

Energyk;jt ¼ Energyk;j

t þEnergyk;it

� broadcast diffusion Neg

� trustij

average total trust� 1

happiness factorjð7Þ

In Eqs. (6) and (7), we can see how much the alter ego

will be influenced by the focal ego (the value of Energytk,j)

is proportional to the trust between ego i and ego j, and

proportional to the happiness factor of the alter ego. Closer

friends with large trust strength influence each other more.

An ego with a larger happiness factor is influenced more by

positive news from its neighbours; however, less by

negative news from its neighbours, vice versa.

When focal ego diffuses negative emotion to its neigh-

bours, as a result, its neighbours sometimes give feedback

to this negative emotion to the focal ego as a comfort

(social support). This comfort decreases the energy of the

negative emotion for the focal ego. This comfort only

happens when the alter ego has higher happiness level than

the focal ego and stops when this negative energy reduces

to zero. The formula for emotion comfort is

Energyk;jt ¼ min

�

0;Energyk;jt þMaxð0; happiness diffijÞ

� comfort multiplier � happiness factorj

� trustijaverage total trust

�

ð8Þ

where comfort_multiplier is multiplier for of comfort

which is ranging from 0 to 1 and happiness_diffij is the

happiness difference between ego i and ego j:

happiness diffij ¼ happinessi � happinessj ð9Þ

where happinessi and happinessj are the happiness for ego

i and ego j, and the happiness for each ego is defined as the

accumulation of all its emotions:

happinessi ¼XMi

m¼1

Energym ð10Þ

where Mi is the total number of emotions for ego i and

Energym is the energy for the mth emotion for ego i.

Similarly, positive emotion can get positive resonance

depending on the happiness level of the alter ego if emotion

energy is positive:

Energyk;jt ¼ Energyk;j

t þMaxð0; happiness diffijÞ� resonance multiplier � happiness factorj

� trustijaverage total trust

ð11Þ

In Eq. (8) and (11), we assume that comfort and

resonance only happen when the alter ego has higher

happiness level than the focal ego. If the alter ego is

unhappy, it has no capability/mood to comfort the focal

ego or resonance to the focal ego’s happiness to make the

focal ego happier.

5 SBH social network simulation results and analysis

In this section, a social network with 200 egos is generated

from SBH simulator. We use SBH simulator to generate a

292 D. Wang et al.

123

social network because SBH is a trust-based social net-

work, which we can use to investigate emotion diffusion

process without redefining trusts between egos. Another

benchmark social network structure, small network is

investigated in the next section. In a social network, dif-

ferent egos have their different number of neighbors and

different trust distribution among their neighbors. In

addition, different egos have their different personal char-

acter settings and background settings as discussed in

Sect. 4.1. We set 200 turns, and in each turn, each indi-

vidual get a chance to come across event and spread its

recent emotion to its direct neighbors based on probability

(as discussed in Sects. 4.2 and 4.3). The amount of emotion

energy received by the alter ego is discussed in Sect. 4.3.

In the following sub-sections, we change the social

parameters (discussed in Sect. 4.2) to see the dynamic

emotion diffusion and its result on happiness level.

5.1 Event probability versus emotion diffusion

probability

First, we analyze the sensitivity for the parameters of event

probability and emotion diffusion probability. In this sec-

tion, we set the parameters:

Diffusion factor for positive emotion = 0.8

Diffusion factor for negative emotion = 0.8

Comfort factor = 0.8

Resonance factor = 0.8

We set the above four parameters as comparatively lar-

ger values to see the apparent difference for the results.

Different values for above four parameters are discussed

and analyzed in the following subsections. We change the

parameters of event probability from 0 to 1 and change

emotion diffusion probability from 0 to 1. If event proba-

bility = 0, no event happens to any ego and no emotion

diffuses through the social network. The happiness level is a

flat line in this case, which is out of our interest. So we do

not report the result for event probability = 0. The report

for event probability = 0.2, 0.6, 1.0 and different values for

emotion diffusion probability are reported in Fig. 1. Fig-

ure 1a–c report the average happiness level for the whole

population. In each figure, emotion diffusion probability

changes from 0 to 1. We can see from Fig. 1a–c, the average

happiness level for the whole population increases with the

increase of emotion diffusion probability. In addition, with

the increase of event probability, the increase of happiness

level with the increase of emotion diffusion probability

becomes more obvious. For example when event proba-

bility = 0.2 the happiness level is enlarged to 0.6 when

emotion diffusion probability = 1. However, when event

probability = 1.0 the happiness level is enlarged to 1.3

when emotion diffusion probability = 1.0.

The conclusion is that, first, if event probability is fixed,

in other words, if the outside events happen to all egos at a

known frequency, increasing emotion diffusion probability

helps in increasing the happiness level for the whole social

network due to the happiness sharing and emotion support.

Secondly, increasing event probability, in other words, if

events happen more frequently to all egos, the happiness

level for the whole social network increase more due to

more happiness to share and more support an ego can get

from its neighbors. This conclusion is consistent with the

literature: more social support helps to increase individ-

ual’s happiness level.

5.2 Diffusion factor for positive emotion

versus diffusion factor for negative emotion

In this section, we set the parameters as

Event probability = 0.8

Emotion diffusion probability = 0.8

Comfort factor = 0.8

Resonance factor = 0.8

Then, we change the parameters of diffusion factor for

positive emotion and negative emotion from 0.2 to 0.8. The

result is reported in Fig. 2. Diffusion factor for positive

emotion indicates how much the alter ego is influenced by

the focal ego for positive event/information; and Diffusion

factor for negative emotion indicates how much the alter

ego is influenced by the focal ego for negative event/

information. In this simulation, as shown in Fig. 2, it is not

surprising that larger diffusion factor for positive emotion

and smaller diffusion factor for negative emotion result in

higher average happiness level for the whole population.

Till now, there is no obvious evidence showing whether

positive emotion or negative emotion has more influence in

emotion diffusion process. It is not clear if the influences

are different, which has more influence over the other and

how much the difference is. These unsolved problems need

further research on social psychology. If we keep diffusion

factor for positive emotion and diffusion factor for negative

emotion as the same, the result is shown in Fig. 3. We can

see from Fig. 3, higher values of diffusion factors for both

positive and negative emotion result in a slightly higher

average happiness level for the whole population, which

indicates more social support helps in increasing happiness

level for the society again.

5.3 Comfort factor and resonance factor

In this section, we set the social parameters as

Event probability = 0.8

Emotion diffusion probability = 0.8

A trust-based multi-ego social network model 293

123

Fig. 1 Happiness comparison

for different values of event

probability and emotion

diffusion rate Y axis is turns and

X is the happiness level

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4 0.2-0.20.2-0.40.2-0.60.2-0.80.4-0.20.4-0.40.4-0.60.4-0.80.6-0.20.6-0.40.6-0.60.6-0.80.8-0.20.8-0.40.8-0.60.8-0.8

0 50 100 150 200 250

Fig. 2 Comparison for

different combination of

diffusion factor for positive

emotion and diffusion factor for

negative emotion: positive–

negative; Y axis is turns and X is

the happiness level

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.2-0.20.4-0.40.6-0.60.8-0.80 50 100 150 200 250

Fig. 3 Comparison for same

combination of diffusion factor

for positive emotion and

diffusion factor for negative

emotion: positive–negative;

Y axis is turns and X is the

happiness level

294 D. Wang et al.

123

Diffusion factor for positive emotion = 0.8

Diffusion factor for negative emotion = 0.8

We change the parameters of comfort factor and reso-

nance factor from 0.2 to 0.8. We set as the same values for

comfort factor and resonance factor in our simulation.

Comfort factor and resonance factor indicate the conse-

quence of emotion diffusion through social network, as

social support and happiness sharing. Higher value for

comfort factor indicates higher social supports. Higher

value for resonance factor indicates higher emotion shar-

ing. The comparison results are shown in Fig. 4. From

Fig. 4, we can see higher values for comfort factor and

resonance factor result in higher average happiness level

for the whole population, which supports the literature that

more social support help increase happiness level.

5.4 Happiness level through difficult time

In previous discussion, the initial energy for events is

randomly generated in the range of -1 and 1. In this

section, we change the event generation scheme: the initial

energy for events is randomly generated in the range of

-1.5 and 0.5, which means that more negative events

happen to the whole population in a period.

The social parameters are set as:

Diffusion factor for positive emotion = 0.8

Diffusion factor for negative emotion = 0.8

Comfort factor = 0.8

Resonance factor = 0.8

We change the event probability from 0.2 to 0.8 and

change the emotion diffusion probability from 0 to 1. The

comparison results are shown in Fig. 5. Figure 5a is the

result when we set event probability as 0.2. From Fig. 5a,

we cannot see much difference in average happiness when

we set event probability as 0.2 and change the emotion

diffusion probability. Figure 5b is the result when we set

event probability as 0.8. From Fig. 5b, we can see when we

increase the value for event probability to 0.8, there is

obvious difference in average happiness when we change

the emotion diffusion probability. Based on the simulation

result, the conclusion is that in difficult time (many nega-

tive events happen in comparatively high frequency, e.g.,

when we set event probability = 0.8), emotion diffusion

and social support relieve suffer and increase the happiness

level for the whole population in some degree.

If negative events happen more frequently (e.g. event

probability = 0.8), emotion diffusion and social support

(up to emotion diffusion probability = 0.6) help in

increasing happiness level for the whole population and

make them easy to get through the difficult time. However,

more emotion diffusion (emotion diffusion probabil-

ity [ 0.6) cannot beat the spreading of sore any more i.e.

the extreme parameter emotion probability = 1 does not

result in high happiness level when negative events happen

day by day (event probability = 0.8). We explain this as

follows. In a very hard period, unfortunate things happen in

a high frequency (at probability of 1) and emotion diffu-

sion, resonance and comfort are all high values (all 0.8),

then negative emotions spreads to its neighbours in the next

turn and then to the neighbours’ neighbours (neighbours’

neighbours also include the focal ego itself) following on.

If unhappiness things keep happening, happiness levels for

all egos are decreasing. In that case, no emotion comfort

happens, however, negative emotion diffusion keeps hap-

pening, which decreases the focal’s happiness level again

and again, finally result in the worst result in happiness

level.

5.5 Who are the happiness ones and unhappiness ones

In our previous discussion, we look at the happiness level

in group level. In this section, we analyze the happiness in

individual level. We investigate who are prone to happier.

In other words, we look into whether better personal

character or better initial happiness level, or more friends

results in higher happiness level.

In this simulation, we set the parameters as:

Event probability = 0.8

Emotion diffusion probability = 0.8

Diffusion factor for positive emotion = 0.8

Diffusion factor for negative emotion = 0.8

Comfort factor = 0.8

Resonance factor = 0.8

We rank the happiness level for all individuals and look

into the ones which are happiest and which are unhappiest.

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 50 100 150 200 250

0.2-0.20.4-0.40.6-0.60.8-0.8

Fig. 4 Comparison for same

combination of comfort factor

and resonance factor:comfort

factor: resonance factor; Y axis

is turns and X is the happiness

level

A trust-based multi-ego social network model 295

123

We list the five happiest egos in Table 1 and the five

unhappiest egos in Table 2. We report their happiness

factor (which indicates personal character: whether he is a

happy guy determined by genes), initial happiness (which

indicates the background), the number of friends, and the

average happiness factor for friends (which indicate whe-

ther this ego is surrounded by happy people or unhappy

people).

From Table 1, we can see all happiest egos have higher

happiness factor (larger than 1, happiness factor = 1

means normal happiness level) and all of them have more

friends than average (the average friends number for the

whole population is 14.38). In contrast, three of the

unhappiest egos have lower happiness factor (smaller than

1) and three of the unhappiest egos have fewer friends

(fewer than average 14.38). However, the initial happiness

level has some, but limited influence on the individual

happiness level. We can see the average initial happiness

level for the happiest group is higher than that for the

unhappiest group. However, there is individual ego (ego

275) with lower initial happiness level, but being in the

happiest group due to higher happiness factor and more

friends (hence more happiness sharing and more social

support). The average happiness factor for friends is similar

for the happiest group and the unhappiest group. That is

because in our simulation, each ego has equal probability

to have either happy friends or unhappy friends. Averagely

speaking, each ego is expected to have friends with similar

average happiness factors. Individual happiness for pre-

defined happy and unhappy group will be investigated in

our future work.

To summarize in general, happiness factor (which is

determined by genes) and social support (which is repre-

sented by the number of friends) are two important factors

to determine individual happiness. However, an individ-

ual’s background has limited influence on individual hap-

piness. From this simulation, we can conclude that social

support and emotion sharing help in increase individual

happiness level again.

6 Results and analysis for a benchmark social network:

small network

This part is a supplement of Sect. 5 to show our conclusion

more generally on who are happier. We look into a

benchmark social network structure, small network, in this

sub-section (Watts and Strogatz 1998). Our proposed

-1.8-1.6-1.4-1.2

-1-0.8-0.6-0.4-0.2

00 50 100 150 200 250

diffusion = 0diffusion = 0.2diffusion = 0.4diffusion = 0.6diffusion = 0.8diffusion = 1

(a) event probability = 0.2

-4.5-4

-3.5-3

-2.5-2

-1.5-1

-0.50

0 50 100 150 200 250

diffusion = 0diffusion = 0.2diffusion = 0.4diffusion = 0.6diffusion = 0.8diffusion=1

(b) event probability = 0.8

Fig. 5 Happiness level

comparison in difficult time:

Y axis is turns and X is the

happiness level

Table 1 The happiest egosEgo ID Happiness

factor

Initial

happiness

Number

of friends

Average happiness

factor for friends

267 1.31 0.31 18 1.13

275 1.30 -0.43 19 1.05

47 1.17 -0.16 18 1.00

181 1.340 0.00 18 0.92

241 1.18 0.00 18 1.18

296 D. Wang et al.

123

emotion diffusion method applies trust-based social net-

work. We do not look into more benchmark networks

because there is no obvious trust definition for relationships

within those benchmark networks.

In our experiment, we set n = 20, k = 4 and p = 0.5 for

a small network. The resulting small network is shown in

Fig. 6. In our experiment, we simply define the trust as

inverse proportion to distance for a link. trustij = 100/distij,

where trustij and distij are the trust and distance between

ego i and ego j. As we discussed, we only consider friends/

family members with strong trust strength for emotion

diffusion. If we set the trust threshed as 40 to define a

strong relationship, then we only consider ties with dis-

tance less than 3.

Other parameters are set the same as those in Sect. 5.5

and then we analyze who are happier in this small network.

Event probability = 0.8

Emotion diffusion probability = 0.8

Diffusion factor for positive emotion = 0.8

Diffusion factor for negative emotion = 0.8

Comfort factor = 0.8

Resonance factor = 0.8

We rank the happiness level for all individuals and look

into the ones which are happiest and which are unhappiest.

We list the four happiest egos in Table 3 and the four

unhappiest egos in Table 4. We report their happiness

factor, initial happiness and the average happiness factor

for friends.

From Tables 3 and 4, we can get the same conclusion as

Sect. 5.5. All happiest egos have higher happiness factor

and initial happiness level and have more friends aver-

agely. In contrast, all unhappiest egos have averagely lower

happiness factor and initial happiness level and have fewer

friends than those who are happiest.

Although we can get the same conclusion as in Sect. 5,

I believe Sect. 5 is more persuadable and useful because

SBH presents a more realistic social network structure

(Dunbar 1996, 1998).

7 Conclusion and future work

In this paper, we propose a computational model: trust-

based multi-ego social network. When compared from

previous research, we use multiple agent technique to

investigate and understand the dynamic emotion diffusion

process and the result in happiness level. We investigate

the happiness for both individual level and group level. The

key advantage of our proposed computational model is that

it is able to answer two questions by this dynamic simu-

lation. First, we answer ‘why’ question: why some indi-

viduals are happier than others. We could say people are

happier because they have better happiness gene or more

friends and supports. Secondly, we answer ‘what…if’

question by changing the parameter setting for the model.

If given more social support, an individual who is not born

with a very good background however is a happy person

(with happiness gene) is able to become very happy. The

answer of ‘what…if’ question help us to get a direction to

make policies and take actions to improve the happiness

level of the whole society.

Another novel point of this paper is that, emotions are

considered as energies generated by events from either

outside or inside world and shorten by contracting effect

through time, spread and resonance among social network

Table 2 The least happy egosEgo ID Happiness

factor

Initial

happiness

Number

of friends

Average happiness

level for friends

186 0.54 -0.27 13 1.03

217 1.31 -0.41 16 1.05

245 0.79 -0.38 12 1.07

172 0.81 -0.41 15 1.03

261 1.27 0.03 11 0.94

Fig. 6 A small network (n = 20, k = 4, p = 0.2)

A trust-based multi-ego social network model 297

123

in some degree in a period, and as a consequence change

the happiness level of involved individuals in the social

network. Negative emotions sometimes can get feedback as

comfort, and as a result the unhappiness level of the focal

ego can be softened through this comfort, which simulate

the social support. Positive emotions sometimes can get

positive resonance in some degree which is happiness

sharing among family and friends.

From the simulation results, we can conclude that,

firstly social support does help increase the happiness

level of both individuals and the group; secondly, indi-

viduals with high happiness factor (who have happy

genes) and individuals with more friends (hence more

social support and emotion sharing) tend to be happier;

thirdly a high initial happiness level (which is determined

by background) has limited influence on happiness level.

In other words, an individual who is not born with very a

good background however is a happy person (with hap-

piness gene) and has many social support is able to

become very happy through emotion sharing and social

support. All these conclusions are consistent with the

literatures and proven by our dynamic emotion diffusion

experiments.

In our current work, we do not include comparison

psychology and adaption psychology theory which need

more complicated model, however, are more useful. In

addition, carefully designed questionnaire and further

research on social psychology need to be carried out which

is our future work.

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