Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

Designing experiments on networks

Abstract: Designing experiments on networks challenges an assumption common in classical experimental designs, which is that the response observed on a unit is unaffected by treatments applied to other units. This assumption is referred to as 'non-interference'. This thesis aims at improving the design efficiency and validity of networked experiments by relaxing the non-interference assumption, where efficiency stands for low variance of the estimated quantities (precision) and validity for unbiased quantities (accuracy). We develop flexible and effective methods for designing experiments on networks (with a special focus on social networks) by combining the well-established methodology of optimal design theory with the most relevant features of network theory. We provide evidence that conventional designs such as randomised designs are inefficient compared to a systematic approach that accounts for the connectivity structure that underlies the experimental units. We investigate the impact of the network structure on the efficiency and validity of the experimental design. There is evidence that the experimental design is determined by the small-scale properties of networks. We also develop an algorithmic approach for finding efficient designs by utilising the network symmetry as defined by the automorphism group of the underlying graph. This approach reduces considerably the search time for finding a good design in moderate-sized networks. It works by decomposing the network into symmetric and asymmetric subgraphs and consequently decomposing the design problem into simpler problems on these subgraphs. Moreover, we suggest a framework for finding optimal block designs, while taking into account the interrelations of groups of units within a network. In doing so, the units are initially divided into blocks, using spectral clustering techniques and the concept of modularity, prior to assigning the treatments. We study how the structural properties of the network communities affect the optimal experimental design and its properties. We also make a transition from experiments on social networks to experiments in agriculture showing the diversity of applications this research can address. In particular, we obtain optimal designs with two blocking factors while handling different definitions of neighbour structures related to either the distance among plots or the farmer operations. Throughout this thesis, several optimal designs on networks are obtained using a simple exchange algorithm, which is implemented in the R programming language.

Social Network and Temporal Myopia

Abstract: This paper examines the link between the social networks surrounding business leaders and temporal myopia in strategic planning. Specifically, we hypothesize that processes characteristic of being ...

Opinion-Based Centrality in Multiplex Networks: A Convex Optimization Approach

Abstract: Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of other persons. In this paper, we build upon this observation to propose a new nodal centrality measure for multiplex networks. Our measure, called Opinion centrality, is based on a stochastic model representing opinion propagation dynamics in such a network. We formulate an optimization problem consisting in maximizing the opinion of the whole network when controlling an external influence able to affect each node individually. We find a mathematical closed form of this problem, and use its solution to derive our centrality measure. According to the opinion centrality, the more a node is worth investing external influence, and the more it is central. We perform an empirical study of the proposed centrality over a toy network, as well as a collection of real-world networks. Our measure is generally negatively correlated with existing multiplex centrality measures, and highlights different types of nodes, accordingly to its definition.

New Direction in Degree Centrality Measure: Towards a Time-Variant Approach

Abstract: Degree centrality is considered to be one of the most basic measures of social network analysis, which has been used extensively in diverse research domains for measuring network positions of actors in respect of the connections with their immediate neighbors. In network analysis, it emphasizes the number of connections that an actor has with others. However, it does not accommodate the value of the duration of relations with other actors in a network; and, therefore, this traditional degree centrality approach regards only the presence or absence of links. Here, we introduce a time-variant approach to the degree centrality measure — time scale degree centrality (TSDC), which considers both presence and duration of links among actors within a network. We illustrate the difference between traditional and TSDC measure by applying these two approaches to explore the impact of degree attributes of a patient-physician network evolving during patient hospitalization periods on the hospital length of stay (LOS) ...