Weak Ties Are Surprising Everywhere

Iaakov Exman, Asaf Yosef and Omer Ganon

Software Engineering Department, The Jerusalem College of Engineering – JCE - Azrieli, Jerusalem, Israel

Keywords: Weak Ties, Surprise, Relevance, Knowledge Discovery, Social Network, Automatic Luck Generation,

Keyword Clouds, Keyword Frequencies, Semantic Distance, Topology, Target Task, Customer, Followers.

Abstract: Weak ties between people have been known as surprisingly effective to successfully achieve practical goals,

such as getting a job. However, weak ties were often assumed to correlate with topological distance in virtual

social networks. The unexpected novelty of this paper is that weak ties are surprisingly everywhere,

independently of topological distance. This is shown by modelling luck with reference to a target task, as a

composition of a surprise function expressing weak ties and a target relevance function expressing strong ties

between people. The model enables an automatic luck generation software tool, to support target tasks mainly

by the surprise function. The main result is obtained by superposing the luck model upon network topological

maps of customer relationships to its followers in any chosen social network. The result is validated by

surprise Keyword Clouds of customer followers and Keyword Frequencies for diverse followers. Results are

illustrated by a variety of graphs calculated for specific customers.

1 INTRODUCTION

Two important roles of Online Social Networks are

often treated as distinct and separate: 1- as a huge

source of virtually any discipline knowledge; 2- as an

information source on the network members.

We claim that these two network roles are dual

and mutually benefit from each other. Indeed, in a

recent paper (Exman, Ganon, Yosef, 2020), network

members were modelled by functions estimating the

potential luck for successful completion of chosen

tasks, e.g. product marketing or finding people that

help one to get a job. The functions’ input was the

discipline knowledge specific to the chosen task.

A central modelling assumption was

Granovetter’s hypotheses (Granovetter, 1973). First,

the tie strength between two individuals is directly

proportional to their friendship networks overlap.

Second, weak ties to other people may be more

significant than strong ties for certain tasks.

This paper further investigates the online social

network dual roles. Network members are

characterized both by their chosen task relevant

knowledge and by their network topology. It turns out

that weak ties are a dominant factor for potential

successful completion of chosen tasks.

1.1 Weak Ties in Online Social

Networks

Our previous work (Exman, Ganon, Yosef, 2020)

defined weak ties between any pair of persons as the

amount of semantic content mismatch between the

pair of persons, relative to a given task. We called this

semantic content mismatch the Surprise.

Analogously we also defined strong ties between

any pair of persons as the amount of semantic content

match between the pair of persons, relative to a given

task. We called this semantic content match the

Relevance.

Semantic content in both previous definitions is

characterized by keyword sets for each person,

relative to a keyword set of the chosen task context.

We emphasize that the above definitions, do not

involve any notions of geographical or topological

distances between pairs of persons. In the more

formal section 3 of this paper we refer to an idea of

semantic content distance.

1.2 Automatic Generation of Luck

Informally, our definition of the potential Luck for

successful completion of a chosen task is a

composition of the Relevance with the respective

Surprise for a given pair of persons.

218

Exman, I., Yosef, A. and Ganon, O.

Weak Ties Are Surprising Everywhere.

DOI: 10.5220/0010117202180226

In Proceedings of the 12th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2020) - Volume 1: KDIR, pages 218-226

ISBN: 978-989-758-474-9

The intuitive idea behind this definition is that

potential Luck should certainly be relevant to the

chosen task. But Relevance alone would be totally

deterministic, and probably it would not be enough,

to realistically cover the semantic content variety of

people involved in the online social network

interactions. One also needs an element of

unexpectedness, as given by a calculated Surprise.

We were inspired by a previous definition of

Interestingness (Exman, 2009).

This positive pragmatic approach to Luck – as a

systematic effort to attain successful completion of

tasks, by possibly automatic software tools – is very

different from the derogatory notion of Luck as

obtaining undeserved results, by mere chance.

1.3 Online Social Networks Topology

In this paper, overall views of online social networks

are displayed by network topological maps – i.e.

graphs with indirect, unweighted edges – standing for

any possible kind of interaction among members of

the social network, where vertices represent network

members. Network topological maps are presented in

the results Section 4.

1.4 Paper Organization

The remaining of this paper is organized as follows.

We concisely review Related Work in section 2. Luck

modelling by Surprise and Relevance, is more

formally defined in section 3. The central novelty of

the paper, viz. that weak ties are ubiquitous and the

most significant factor to generate Luck, is presented

in section 4. The design and implementation of the

Luck’o’mation software tool appears in section 5.

The Luck model is validated in section 6. We

conclude the paper with a discussion in section 7.

2 RELATED WORK

This section concisely reviews the scientific literature

on Luck, ties strength and social networks’ topology.

2.1 Systematic Luck

As already stated, our positive pragmatic view of

Luck is very different from the negative stereotype of

undeserved resources acquisition by mere chance.

The book by the late Clayton Christensen and co-

authors (Christensen et al., 2016) entitled

“Competing against Luck” is an extended example of

the negative meaning of Luck. It promotes causality

in contrast to random hit-and-miss development of

new products.

Liechti (Liechti et al., 2012) defines luck with

some similarity to our “surprise”. It is a sum of three

terms standing for an unexpected performance:

 actual deviation from expected performance;

 an overconfidence bias;

 a look back bias (the expectation at a certain

time t minus that at a previous time).

Dowding (Dowding, 2003, 2008) focuses on

moral aspects of luck. His proposed luck measure

expresses a relationship between expected value of

outcome (EV) and an actual outcome (AV):

Luck AV EV





(1)

In a series of measurements, one expects AV to

approach EV.

2.2 Social Networks’ Ties Strength

Granovetter (Granovetter, 1973, 1983) proposed

Weak Ties as a significant notion in social networks.

He also pioneered the application of his theory

(Granovetter, 1995) in the context of “Getting a Job”.

Various studies of weak ties in social networks

supported the theory – such as (Brown, Konrad,

2001), (DeMeo et al., 2014). The book by Ferguson

(Ferguson, 2018) analyses networks in general from

an historical point of view. Its Chapter 6 explicitly

deals with weak ties. Other authors extended the

theory to different applications, – such as (Baer,

2010), (Centola, 2007) – or provided general

appraisals e.g. (Sinan, 2016).

On the other hand, there were researchers that

emphasized the importance of strong ties – such as

(Gee et al., 2017) and (Krackhardt, 2003).

Measurement of tie strength is dealt with in the paper

by (Marsden, Campbell, 1984).

Within the “Getting a Job” context, besides

Granovetter, we can mention (Gee et al., 2017) and

the paper by Tassier on “Labor Market implications

of Weak Ties” (Tassier, 2006).

2.3 Related Social Networks’ Topology

There are three kinds of information available about

online social networks:

a) Specific Grouping of Edges – e.g. triples of

vertices as opposed to transitive triangles.

b) Topological Distance Characterization –in

terms of discrete edge numbers between

vertices;

Weak Ties Are Surprising Everywhere

219

c) Functional Distance Characterization – as

a continuous function, e.g. exponential;

(Mattie et al., 2018) discusses a particular

grouping of edges, which they call “bow tie”, and

infer their tie strength.

(Tassier, 2006) as an example of the functional

distance characterization, states that weak ties in

social networks grow with distance exponentially

faster than strong ties.

3 LUCK GENERATION FROM

WEAK TIES

In this section – whose definitions are partly based

upon our previous paper (Exman, Ganon, Yosef,

2020) – we formalize the concepts of Luck, and its

two components Relevance and Surprise. Then the

respective formulas of match and mismatch are

inserted into the Relevance and Surprise, to enable

actual calculation of numerical values.

3.1 The Luck Model: Strong Ties

Relevance & Weak Ties Surprise

We start by making an assumption, based on (Tassier

2006) “functional distance characterization”. Our

liberal interpretation – justified by the results

obtained in the next section 4 and validated in the

Luck Model Validation in section 6 – is that the

functional distance is applicable to semantic distance:

 Complementary Exponential Decay of Ties –

strong ties decay exponentially with semantic

distance, while weak ties increase

exponentially.

Given this “Complementary Exponential decay”

assumption, Relevance and Surprise are exponential

functions, with complementary signs.

Moreover, by the considerations in sub-section

1.1, the semantic content of Relevance is given by a

match function, while the semantic content of

Surprise is given by a mismatch function. Thus:

Re exp( )levance Match

(2)

exp( )Surprise Mismatch Match

(3)

Since Luck is a composition of Relevance and

Surprise, we finally get:

Luck =

exp( ) exp( )

atch Mismatch Match





(4)

The “plus” operator is the suitable composition of

Relevance and Surprise. A “multiplier” operator is

unsuitable, as it would cause undesirable exponents

addition, and Match cancellation.

In practice, one still needs to normalize the

expressions of Match and Mismatch (see the next

sub-section), to eliminate dependence on set sizes.

3.2 Keyword Sets: Match & Mismatch

We begin by defining some necessary concepts.

Context is a keyword set defining a task, e.g. “find

a job as a knowledge engineer”.

Next the two online social network member roles,

for the same social network, are defined, with their

respective notations:

 Customer = C – is a person demanding the

performance of the Context task; (also its

keyword set);

 Follower = F – a Customer follower in the

social network sense; (also its keyword set);

F can be a Follower of a Follower, etc. to

any network topological distance from the

Customer.

The Context keyword set is fixed before any

computation. The keyword sets of the Customer and

of each Follower are sub-sets of the Context. These

are extracted from Social Network member pages,

and subsequent calculation of their intersections with

the Context keyword set.

Match and Mismatch are keyword set operations

obtaining respectively the Relevance and Surprise

functions, by comparing Customer C keyword sets

with a Follower F keyword set.

Match calculates a similarity measure of the input

sets, i.e. the number of keywords appearing in the

intersection



of these sets:

atch C F





(5)

Mismatch calculates the sets’ dissimilarity, viz.

the numerical symmetric difference



between C

and F. It is the union



of the relative complements

of these sets:

()()

ismatch C F C F F C



  

(6)

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220

Fig.1 shows a schematic Match and Mismatch

diagram.

Figure 1: Schematic Match and Mismatch diagram – C

stands for the Customer keyword set (light blue). F is the

Follower keyword set (gray). Match is the intersection F



C. Mismatch is the union between the relative complements

C-F and F-C. (All figures are in color online).

4 WEAK TIES SURPRISE

EVERYWHERE

This central section of this paper shows the novel

significant results of this work.

As a preview, here are the results:

 Weak Ties – represented by the Surprise

function – have a much more significant

contribution than Relevance, to the

numerical values of the calculated

potential Luck;

 Surprise – is ubiquitous, i.e. it appears

everywhere throughout the network,

independently of the topological

distance.

So, this is a double surprise: the overwhelming

importance of weak ties and its ubiquity.

4.1 Luck vs Surprise

In this sub-section one can see the first computation

result of this paper. The social network was chosen

according to an available API. The computation

refers to the Context task “find a job as Software

Engineer”.

The Context Keyword Set used in the

computations is seen in the next text-box.

Match and Mismatch functions normalization in

equation (4) was done as follows: dividing the non-

normalized outcome by a sum of the Context and

Costumer keyword sets intersection, with the Context

and each Follower keyword sets intersection.

Fig. 2 shows a plot of Luck against Surprise for

the data-set of a certain Customer JS.

Figure 2: Plot of Luck vs. Surprise for Customer JS – The

dots (in orange colour) are computation results for this data

set. The trend-line is a very good polynomial fitting.

The plot in Fig. 2 displays the following features:

 Surprise, for Weak Ties, definitely increases

when Luck increases (right-hand side of

plot);

 Relevance, for Strong Ties, moderately

increases, causing a smaller Luck increase

(left-hand-side of the plot).

The graph asymmetry is very clear.

This plot is important since the same functional

behaviour has been repeatedly found for all plots of

this kind for a variety of different customers – see e.g.

fig. 4 in our previous paper (Exman, Ganon, Yosef,

2020).

4.2 Online Social Networks Topology

Maps

In this paper, online social networks topology is

represented by “maps” – which mathematically are

graphs with indirect, unweighted edges, between

vertices. The vertices stand for members of the social

Software, engineering, developer, DevOps, computers,

algorithm, TechOps, python, programmer, java, ‘computer

science’, ‘data science’, ‘data analyse’, C++, web,

framework, embedded, ‘alpha version’, API, api, app,

application, beta, version, bios, QA, automation, agile,

scrum, demo, development, device, emulator, freeware,

‘open source’, interface, ‘operating systems’, workflow

‘machine learning’, ‘deep learning’, startup,

innovation,

internet, IoT, VR, code, coding.

Weak Ties Are Surprising Everywhere

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network, and the edges represent any possible kind of

interaction among members of the social network.

Features that may be perceived in the network

topological maps, are small clusters of the immediate

followers, or more distant, followers of followers for

any given members in the same network. Thus, one

can naturally have an idea of the proximity levels of

network members in the map.

In order to display and understand the results

obtained in this paper, we do not consider necessary

to focus on more specific structures within the

network topology map, such as vertex triples or bow-

ties as mentioned in the Related Work sub-section

2.3.

4.3 Surprise Is Everywhere in Network

Topology Maps

A partial overall view of an online social network

topology map centred on another customer LM is

seen in Fig. 3. The view is partial, in the sense that it

was limited by the number of follower levels (up to 8

levels) of the given customer.

Vertices were shown coded by three colours:

 Green – the Customer;

 Purple – Customer followers, whose

Surprise value is above a certain

threshold;

 Blue – any other social network

members.

One perceives 1

level followers’ clusters in

several areas of the social network topology map.

The central result shown here is:

 Customer followers with a high Surprise

value are everywhere in this network

topological map: Surprise is independent of

topological distance from the customer.

This result was consistently obtained for many

different Customers, not necessarily semantically or

topologically related, and whose followers do not

significantly overlap network followers of the other

Customers. We purposefully selected independent

Customers to demonstrate the obtained result.

Figure 3: Surprise Social Network Topology Sample Map

for Customer LM – The customer (in green) is seen in the

lowest cluster. Customer Followers with high-value

Surprise (in purple) are seen everywhere, i.e. in an

overwhelming number of clusters in the network topology

map.

5 LUCK’O’MATION DESIGN

AND IMPLEMENTATION

Luck’o’mation is a software tool designed and

implemented to run calculations of potential Luck,

Surprise and Relevance, in order to test and validate

the model proposed in this work.

It is an improved functionality and more efficient

version of the software tool described and used for

our previous work (Exman, Ganon, Yosef, 2020).

5.1 Software Design

The Luck’o’mation Sofware tool has well-designed

modules with independent roles:

1. Front-End – for text and graph input/output;

2. Command – for efficient running of common

options;

3. APIs – for interaction with any chosen social

networks;

4. Local Storage – avoiding repeated network

access, and an Inquirer to retrieve stored data;

5. Calculators – of Tie Strength and Luck.

The Luck’o’mation software architecture is seen in

Fig. 4.

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Figure 4: Luck’o’mation Software Architecture – The five

independent modules are marked by different colors: 1-

Front-End (yellow); 2- Command (purple); 3- APIs (blue);

4- Local Storage (orange); 5- Calculators (green).

5.2 Software Implementation

Luck’o’mation is programmed in the Python

language. A user interacts with the software tool by

means of a CLI (Command Line Interface) to run

different simulations and scripts to analyse data.

Upon execution, the software builds a network

map (unweighted, undirected graph) based on the

data available from the input and store it in the RAM

for data manipulation and visualization.

Libraries used in the software include:

 Network API – used to collect data from

the social network;

 Networkx – used to create graphs and

analyse them;

 Matplotlip – used to visualize graphs;

 Click, PyInquirer – used to create the CLI

for any user to be able to run simulations

and data analytics easily.

The database used is Sqlite to store the data

collected from the social network, such as posts,

network members and their connections among other

information.

6 LUCK MODEL VALIDATION

Many facets of this work can serve to validate it. In

this section we present three approaches:

a) agreement with previously published

research;

b) self-consistency of semantic content viewed

through keyword clouds;

c) randomized dilution of followers’ numbers

per customer.

6.1 Independence of Topological

Distance

The Luck model is based upon certain assumptions,

most important among them the Complementary

Exponential decay of weak and strong ties. These

assumptions of the model can be validated by

comparison of model consequences with previous

research.

An unexpected and important result of this work

is the ubiquitous and prominent availability of

Surprise, independently of network topological

distance.

The independence of network topological

distance is confirmed by results obtained by different

methods, e.g. in a paper by (Bhattacharyya, Garg, Wu

2011).

6.2 Self-Consistent Semantic Content

in Word Clouds

Self-Consistency of Results means to obtain similar

outcomes for very different Customers, Followers

and Semantic Content in online social networks.

Semantic content is here calculated as follows.

For each chosen customer in the social network, and

for all its followers in our dataset, calculate surprise

values, extracting the most frequent keywords

contributing to the customer’s surprise.

The most frequent keywords are visualized in a

Keyword Cloud, with letter sizes proportional to

keyword frequencies in the customer followers.

The conclusion of interest is that most of the high-

frequency words are common to all followers of these

customers. These are clearly observed to be: api,

version, demo, application, innovation, internet.

Therefore, the calculated surprise for all these

customers is not just the result of random disjoint

(not-intersecting) sets of keywords. It shows self-

consistent semantic content, which explains the utility

of the calculated surprise to generate luck (success)

for the chosen task.

Keyword Clouds are shown in Fig. 5, for four

different customers and totally independent

followers. The similar keyword clouds of the

customers (CD, MM, SC), can be explained by

network topology paths, linked at a given topological

distance, enabling surprising keywords exchange.

Especially interesting is the isolated LM customer,

Weak Ties Are Surprising Everywhere

223

with common prominent keywords, despite different

followers and less linked paths.

Figure 5: Keyword Clouds of followers of four Customers

– Keywords’ letter sizes are proportional to the occurrence

frequency of each word in the calculated “surprise” for all

followers of each customer. The customer name initials are

seen in the upper-right corner of each cloud.

6.3 Randomized Dilution of Followers’

Number

The hypothesis for this validation approach is as

follows. If surprise is really everywhere in the

topological network, it should be independent of the

specific choice of followers of any given customer.

Figure 6: Randomized Dilution of the followers’ number

for each of the four Customers – No dilution, 100% (blue

data) fits the Keyword Clouds in Fig. 5. Diluted data are

obtained by randomized followers’ shuffling, taking the

upper 70% (red data) and upper 50% (green data) of the

respective surprise keywords for each customer.

Thus, if one performs randomized dilution of the

followers of a customer, the relative frequency

functional behaviour of the followers’ surprise

keywords should remain virtually unchanged.

The dilution experiment was performed for the

same four customers shown in Fig. 5. The followers

of each customer were randomly shuffled according

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224

to a uniform distribution. Then, certain percentages of

the upper followers in the list (70% and 50% in Fig.

6) were selected and their surprise keyword

occurrences were calculated.

Results, seen in the graphs of Fig. 6, show that

the relative surprise keyword frequencies, for each

customer, preserve the same overall functional

behaviour, independently of dilution, corroborating

the hypothesis.

7 DISCUSSION

This discussion focuses on the appraisal of the main

results obtained, viz. the significance and ubiquity of

Surprise in the online social network. It is concluded

by future work to be done, and main contribution.

7.1 The Weak Ties Topology Surprise

The unexpectedness of the prominence of Weak Ties

is a consequence of widely held, but misleading

perceptions. We mention three of these perceptions:

 The very name of “Weak” ties, suggests less

influence than Strong ties, in contrast to

Granovetter’s hypotheses;

 the apparent balance between Weak and

Strong ties as pointed out by a non-

negligible number of authors;

 an initial conjecture of symmetric

exponential decay of Relevance and

Surprise.

But computed results from empirical data

extracted from actual online social networks, in

sections 4 and 6, clearly show the greater importance

and everywhere availability of weak ties.

7.2 Future Work

Future work to be done within this project, include the

following issues:

a. Extensive Data Analysis – since the datasets

accumulated in this work until now are very

large, compared to datasets of previously

published research by other authors, we still

need to invest time in a dedicated analysis;

b. Diverse Social Networks and Datasets – in

order to test the generality and robustness of

the assumptions, one needs to use it with a

few different social networks and additional

datasets, to compare their behaviours and

results;

c. Model Variations – we have used a bag-of-

words modelling approach. We should test

our hypotheses with word embedding

approaches.

7.3 Main Contribution

The main contribution of this work is the ubiquity and

importance of Surprise – standing for online social

network weak ties – as a component of systematic

generation of potential Luck towards successful

completion of chosen tasks.

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