Power and Network Integration

174 Pages·2017·5.4 MB·English

Power and Network Integration:
Structural and Algorithmic Analysis of
Organizational Networks
Anastasia Moskvina
PhD
2016
Power and Network Integration:
Structural and Algorithmic Analysis of
Organizational Networks
Anastasia Moskvina
A thesis submitted to
Auckland University of Technology
in fulfillment of the requirements for the degree of
Doctor of Philosophy(PhD)
2016
School of Engineering, Computer & Mathematical Sciences
Auckland University of Technology
Abstract
This thesis constitutes the results of our research towards structural and algorithmic
analysis of organizational networks. We study how interpersonal ties become crucial
empowerment channels that shape organizational structure. We develop an organi-
zational network model that is consistent with management studies; moreover, by
incorporating both formal and informal ties into the model, we build a promising the-
ory that is capable to explain several organizational phenomena including flattening,
workplace homophily, and loss of control. Through rigorous analysis, we demonstrate
that our theoretical framework can be used to reflect general properties of organiza-
tions.
Understanding how different departments and employees of an organization inter-
act with one another leads to comprehension of how well the organization operates.
Studying an organizational structure often reveals critical positions that may require
additional attention. It is the organizational structure from which one may extract
hidden clues about concealed communication obstacles. In this thesis, we consider or-
ganizational structures from the network perspective. We see the following problems:
(1) There is a lack of mathematical analysis on the dual-structure of formal and
informal organizations.
(2) Existing formal definitions of power only deal with networks whose edges have
a single interpretation of social links, while not incorporating formal roles and
levels.
(3) Network evolution represents a substantial direction of the structural analysis of
social networks but yet there is a lack of models suitable for joining two networks
as an outcome of strategic calculations.
The aim of this thesis, therefore, is to challenge the problems by developing a mathe-
matical model that sits at the confluence of algorithmic and structural analyses. Our
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investigation unfolds in two main directions: the first covers individual power in orga-
nizations; the second lies in integrating two disjoint organizational networks.
The first focal point of this thesis is our centrality-based definition of power which
is accompanied with comprehensive and deep analysis, case studies and experiments.
Our power based model provides novel insights into a range of organizational proper-
ties: 1) Organizations have limited hierarchy height. 2) Flattening is closely related
to changes in the power of employees. 3) Informal relations significantly impact power
of individuals. 4) Leadership styles could be reflected and analyzed through under-
standing weights on the ties in an organizational network. 5) The model endorses a
natural interpretation of the loss of managerial control.
Our second research direction concerns computational and algorithmic aspects of
network integration. The integration process amounts to the fundamental question
that arises in numerous social, political, and physical domains. We study the algorith-
mic nature of network integration, analyze the corresponding computational problems,
apply a formal framework to tackle the problems and employ various heuristics that
reflect natural intuition. To compare the methods, we perform thorough experimental
analysis on both synthesized and real-world data.
The significance of this thesis lies in theoretical models, simulations and analy-
sis. Our novel, structural approach to organizational analysis provides new insights,
explanations and potentially predictive guidelines for organizational decision making.
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Acknowledgments
I would like to express my gratitude to Dr. Jiamou Liu, my supervisor and co-author,
for encouraging my research and being a great mentor. Thank you for your guidance
and profound advice.
I am very grateful to Prof. Ajit Narayanan, my supervisor, for kindness, valuable
support and helpful discussions.
I would also like to thank Michael Ouˇredn´ık for collaboration, interesting sugges-
tions and assistance with implementing software tools. Working with you was a great
pleasure.
This research would not have been possible without the support of the Marsden
Fund of the Royal Society of New Zealand.
Finally, to my dear soulmate and loving husband, Mikhail Kokho, for pushing me
forward and for constructive criticism, for inspiration and for lighting up my path
during this research journey.
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Contents
Abstract iii
Acknowledgments v
List of Figures ix
List of Tables xiii
Attestation of Authorship xiv
1 Introduction 1
1.1 Social Network Analysis and Power in Organizations . . . . . . . . . . 2
1.2 Integration as a Form of Network Evolution . . . . . . . . . . . . . . . 4
1.3 Measures to Evaluate the Effect of Integration . . . . . . . . . . . . . . 6
1.4 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Preliminaries 20
2.1 Social Network Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.1 Defining a Network . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.2 Properties of Social Networks . . . . . . . . . . . . . . . . . . . 21
2.1.3 Centrality Measures . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Organizational Networks: Model and Key Properties . . . . . . . . . . 24
2.3 Small Distance-k Dominating Set . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Four Greedy Algorithms . . . . . . . . . . . . . . . . . . . . . . 28
2.3.2 Simplified Greedy Algorithms . . . . . . . . . . . . . . . . . . . 30
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3 Power in Organizational Networks 32
3.1 Measure of Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.1 What Defines Power: a Network Perspective . . . . . . . . . . . 33
3.1.2 Power, Influence, and Authority . . . . . . . . . . . . . . . . . . 35
3.1.3 Definition of Power . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Stability and Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 Chain Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Perfect Tree Networks . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 Flattening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4 Understanding Informal Ties . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4.1 A Benchmark for Organizational Networks . . . . . . . . . . . . 54
3.4.2 Importance of Informal Ties . . . . . . . . . . . . . . . . . . . . 57
3.5 Leadership Styles: a Network Perspective . . . . . . . . . . . . . . . . . 62
3.6 Case Study: Krackhardt and Hanson’s Network . . . . . . . . . . . . . 67
3.7 CORPNET: an ONA Tool . . . . . . . . . . . . . . . . . . . . . . . . . 69
4 Integrating Homogeneous Networks 72
4.1 Togetherness and Network Integration . . . . . . . . . . . . . . . . . . 73
4.1.1 Three Levels of Togetherness on Integrated Networks . . . . . . 74
4.1.2 The Network Integration Problems . . . . . . . . . . . . . . . . 76
4.1.3 Privilege and Priorities . . . . . . . . . . . . . . . . . . . . . . . 78
4.2 Equal privilege . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.1 Optimizing ∃-togetherness . . . . . . . . . . . . . . . . . . . . . 80
4.2.2 Optimizing ∀-/∆-togetherness . . . . . . . . . . . . . . . . . . . 83
4.2.3 Algorithms for Solving NI (G ,G ) . . . . . . . . . . . . . . . . 85
∆ 1 2
4.3 Priority Based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.4 Socialization as a Special Case of Integration . . . . . . . . . . . . . . . 93
4.4.1 Network Building: the Problem Setup . . . . . . . . . . . . . . 94
4.4.2 Complexity and Algorithms for BROKER . . . . . . . . . . . . . 94
4.4.3 Complexity and Algorithms for DIAM . . . . . . . . . . . . . 98
dm
4.5 Experimental Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.5.1 Solving Network Integration Problems . . . . . . . . . . . . . . 103
4.5.2 Priority Based Methods . . . . . . . . . . . . . . . . . . . . . . 113
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4.5.3 Solving BROKER and DIAM . . . . . . . . . . . . . . . . . . . . 115
5 Integration of Two Organizational Networks 121
5.1 Network Integration in Organizations . . . . . . . . . . . . . . . . . . . 122
5.2 Togetherness in Organizational Networks . . . . . . . . . . . . . . . . . 124
5.2.1 Togetherness as a Local Measure of Proximity . . . . . . . . . . 126
5.2.2 Using Togetherness to Evaluate Integration . . . . . . . . . . . . 129
5.3 Dominant integration of organizations . . . . . . . . . . . . . . . . . . . 130
5.3.1 Dominant Integration with a Single Node . . . . . . . . . . . . . 133
5.3.2 Dominant Integration of Two Hierarchies . . . . . . . . . . . . . 133
5.3.3 Solving the Dominant Integration Problem with Fixed Hierar-
chical Togetherness . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.3.4 Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.4 Collaborative Integration of Two Organizational Networks . . . . . . . 146
5.4.1 Collaborative Integration of Two Hierarchies . . . . . . . . . . . 147
5.4.2 Collaborative Integration of Subnetworks . . . . . . . . . . . . . 148
6 Conclusion and Future Works 150
Bibliography 153
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List of Figures
3.1 Defining power of A, B and C . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 An organizational network (on the left) and its weighted interaction
graph (on the right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Individual power with k = 0.5 (left) and k = 0.1 (right) . . . . . . . . . 40
3.4 Network A with 31 nodes . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Network B with 31 nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 The power of three perfect tree networks with arities 2,3, and 4. The
plots show the power across all levels of the hierarchies. . . . . . . . . . 52
3.7 The average power of nodes across all levels in different random trees
as the hierarchy flattens (left). Each curve corresponds to a particular
level, andthehorizontalaxisreferstothedifferenttrees. Averagepower
of nodes in the last level of these trees (right). Average power of nodes
in the second-to-last level (center). . . . . . . . . . . . . . . . . . . . . 54
3.8 A randomly generated network for d = 3 and 7 levels. Blue and yel-
low lines are formal and informal ties, resp. The root is the brown
square. Sizes of nodes indicates their power. The graph is generated
and visualized by CORPNET. . . . . . . . . . . . . . . . . . . . . . . . 56
3.9 Power of informal ties on community formations in organizations. Clus-
ters are indicated by different colors. The graphs and their clustering
are computed by CORPNET . . . . . . . . . . . . . . . . . . . . . . . . 57
3.10 Random tree and random social network. The graph is generated and
visualized by CORPNET . . . . . . . . . . . . . . . . . . . . . . . . . . 57
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3.11 Average values of power at each hierarchy level in randomly generated
socialnetworks: (a)inthetallorganization, and(b)intheflatorganiza-
tion. The different lines indicate differences in “density” of the informal
ties; in general, a denser informal relation causes a more even distribu-
tion of power across levels, hence a “flattened” (less-steep) curve. . . . 59
3.12 Power (left) and variance (right) for three types of perfect trees with
increasing density of informal ties. . . . . . . . . . . . . . . . . . . . . . 59
3.13 (left) The instability index for three types of perfect trees with informal
ties. (right) The modularity for these networks. . . . . . . . . . . . . . 60
3.14 The results include three types of perfect trees with informal ties. The
horizontal axis for all plots is the density of informal ties in the network.
(left) The average power of the root. (center) The average power of the
leaves. (right) The ratio between the average power of the root against
the leaves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.15 Average power of perfect tree of arity of 4 and height 5 with random
informal ties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.16 Perfect Tree of height 5 with informal ties. (left) The power of the
roots. (center) The variance of power among all nodes. (right) The
ratio between power of roots against leaves. . . . . . . . . . . . . . . . 63
3.17 Perfect Tree of height 5 with informal ties. (left) Modularity of the
identified clusters by Newman’s spectral algorithm. (right) Instability
index of the networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.18 Distribution of power in networks with different management styles . . 66
3.19 Thedistributionofaveragepoweracrossalllevelsinrandomlygenerated
networks. The networks consist of random formal tie hierarchy and
random informal ties. Power in random tall organizations (left) where
theformaltiehierarchyhasheight7andmeanarity3. Powerinrandom
flatorganizations(right)wheretheformaltiehierarchyhasheight4and
mean arity 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.20 Krackhardt and Hanson’s hierarchy with 21 nodes. . . . . . . . . . . . 68
3.21 CORPNET user interface: a tree layout (left) and a force directed layout
with a power distribution (right) . . . . . . . . . . . . . . . . . . . . . 70
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