Dynamics in large scale networks

In this thesis we study the properties of two large dynamic networks, the competition network of advertisers on the Google and Bing search engines and the dynamic network of friend relationships among avatars in the massively multiplayer online game (MMOG) Planetside 2. We are particularly interested in removal patterns in these networks. Our main finding is that in both of these networks the nodes which are most commonly removed are minor near isolated nodes. We also investigate the process of merging of two large networks using data captured during the merger of servers of Planetside 2. We found that the original network structures do not really merge but rather they get gradually replaced by newcomers not associated with the original structures. In the final part of the thesis we investigate the concept of motifs in the Barabási-Albert random graph. We establish some bounds on the number of motifs in this graph.

Heuristics for the Critical Node Detection Problem in Large Complex Networks

Complex networks have recently attracted a significant amount of research attention due to their ability to model real world phenomena. One important problem often encountered is to limit diffusive processes spread over the network, for example mitigating pandemic disease or computer virus spread. A number of problem formulations have been proposed that aim to solve such problems based on desired network characteristics, such as maintaining the largest network component after node removal. The recently formulated critical node detection problem aims to remove a small subset of vertices from the network such that the residual network has minimum pairwise connectivity. Unfortunately, the problem is NP-hard and also the number of constraints is cubic in number of vertices, making very large scale problems impossible to solve with traditional mathematical programming techniques. Even many approximation algorithm strategies such as dynamic programming, evolutionary algorithms, etc. all are unusable for networks that contain thousands to millions of vertices. A computationally efficient and simple approach is required in such circumstances, but none currently exist. In this thesis, such an algorithm is proposed. The methodology is based on a depth-first search traversal of the network, and a specially designed ranking function that considers information local to each vertex. Due to the variety of network structures, a number of characteristics must be taken into consideration and combined into a single rank that measures the utility of removing each vertex. Since removing a vertex in sequential fashion impacts the network structure, an efficient post-processing algorithm is also proposed to quickly re-rank vertices. Experiments on a range of common complex network models with varying number of vertices are considered, in addition to real world networks. The proposed algorithm, DFSH, is shown to be highly competitive and often outperforms existing strategies such as Google PageRank for minimizing pairwise connectivity.

A game-theoretic network formation model

We study the dynamics of a game-theoretic network formation model that yields large-scale small-world networks. So far, mostly stochastic frameworks have been utilized to explain the emergence of these networks. On the other hand, it is natural to seek for game-theoretic network formation models in which links are formed due to strategic behaviors of individuals, rather than based on probabilities. Inspired by Even-Dar and Kearns (2007), we consider a more realistic model in which the cost of establishing each link is dynamically determined during the course of the game. Moreover, players are allowed to put transfer payments on the formation of links. Also, they must pay a maintenance cost to sustain their direct links during the game. We show that there is a small diameter of at most 4 in the general set of equilibrium networks in our model. Unlike earlier model, not only the existence of equilibrium networks is guaranteed in our model, but also these networks coincide with the outcomes of pairwise Nash equilibrium in network formation. Furthermore, we provide a network formation simulation that generates small-world networks. We also analyze the impact of locating players in a hierarchical structure by constructing a strategic model, where a complete b-ary tree is the seed network.

Untangling the Organizational Ambiguities in Supply Chain Risk Recognition, Assessment, and Response: The Role of Network Embeddedness

In this thesis, I focus on supply chain risk related ambiguity, which represents the ambiguities firms exhibit in recognizing, assessing, and responding to supply chain disruptions. I, primarily, argue that ambiguities associated with recognizing and responding to supply chain risk are information gathering and processing problems. Guided by the theoretical perspective of bounded rationality, I propose a typology of supply chain risk related ambiguity with four distinct dimensions. I, also, argue that the major contributor to risk related ambiguity is often the environment, specifically the web of suppliers. Hence, I focus on the characteristics of these supplier networks to examine the sources of ambiguity. I define three distinct elements of network embeddedness – relational, structural, and positional embeddedness – and argue that the ambiguity faced by a firm in appropriately identifying the nature or impacts of major disruptions is a function of these network properties. Based on a survey of large North American manufacturing firms, I found that the extent of the relational ties a firm has and its position in the network are significantly related to supply chain risk related ambiguity. However, this study did not provide any significant support for the hypothesized relationship between structural embeddedness and ambiguity. My research contributes towards the study of supply chain disruptions by using the idea of bounded rationality to understand supply chain risk related ambiguity and by providing evidence that the structure of supply chain networks influences the organizational understanding of and responses to supply chain disruptions.