Statistical Analysis of Network Data with R

Inhaltsverzeichnis

1. Frontmatter

2. Chapter 1. Introduction

   Eric D. Kolaczyk, Gábor Csárdi

   Abstract

   The oft-repeated statement that “we live in a connected world” perhaps best captures, in its simplicity, why networks have come to hold such interest in recent years. From on-line social networks like Facebook to the World Wide Web and the Internet itself, we are surrounded by examples of ways in which we interact with each other. Similarly, we are connected as well at the level of various human institutions (e.g., governments), processes (e.g., economies), and infrastructures (e.g., the global airline network). And, of course, humans are surely not unique in being members of various complex, inter-connected systems. Looking at the natural world around us, we see a wealth of examples of such systems, from entire eco-systems, to biological food webs, to collections of inter-acting genes or communicating neurons.

3. Chapter 2. Manipulating Network Data

   Eric D. Kolaczyk, Gábor Csárdi

   Abstract

   We have seen that the term ‘network,’ broadly speaking, refers to a collection of elements and their inter-relations. The mathematical concept of a graph lends precision to this notion. We will introduce the basic elements of graphs—both undirected and directed—in Sect. 2.2 and discuss how to generate network graphs, both ‘by hand’ and from network data of various forms.

4. Chapter 3. Visualizing Network Data

   Eric D. Kolaczyk, Gábor Csárdi

   Abstract

   Up until this point, we have spoken only loosely of displaying network graphs, although we have shown several examples already. Here in this chapter we consider the problem of display in its own right. Techniques for displaying network graphs are the focus of the field of graph drawing or graph visualization. Such techniques typically seek to incorporate a combination of elements from mathematics, human aesthetics, and algorithms.

5. Chapter 4. Descriptive Analysis of Network Graph Characteristics

   Eric D. Kolaczyk, Gábor Csárdi

   Abstract

   In the study of a given complex system, questions of interest can often be re-phrased in a useful manner as questions regarding some aspect of the structure or characteristics of a corresponding network graph. For example, various types of basic social dynamics can be represented by triplets of vertices with a particular pattern of ties among them (i.e., triads); questions involving the movement of information or commodities usually can be posed in terms of paths on the network graph and flows along those paths; certain notions of the ‘importance’ of individual system elements may be captured by measures of how ‘central’ the corresponding vertex is in the network; and the search for ‘communities’ and analogous types of unspecified ‘groups’ within a system frequently may be addressed as a graph partitioning problem.

6. Chapter 5. Mathematical Models for Network Graphs

   Eric D. Kolaczyk, Gábor Csárdi

   Abstract

   So far in this book, the emphasis has been almost entirely focused upon methods, to the exclusion of modeling—methods for constructing network graphs, for visualizing network graphs, and for characterizing their observed structure. For the remainder of this book, our focus will shift to the construction and use of models in the analysis of network data, beginning with this chapter, in which we turn to the topic of modeling network graphs.

7. Chapter 6. Statistical Models for Network Graphs

   Eric D. Kolaczyk, Gábor Csárdi

   Abstract

   The network models discussed in the previous chapter serve a variety of useful purposes. Yet for the purpose of statistical model building, they come up short. Indeed, as Robins and Morris [1] write, “A good [statistical network graph] model needs to be both estimable from data and a reasonable representation of that data, to be theoretically plausible about the type of effects that might have produced the network, and to be amenable to examining which competing effects might be the best explanation of the data.” None of the models we have seen up until this point are really intended to meet such criteria.

8. Chapter 7. Network Topology Inference

   Eric D. Kolaczyk, Gábor Csárdi

   Abstract

   Network graphs are constructed in all sorts of ways and to varying levels of completeness. In some settings, there is little if any uncertainty in assessing whether or not an edge exists between two vertices and we can exhaustively assess incidence between vertex pairs. For example, in examining one’s own network of Facebook friends, the presence or absence of an edge can be assessed through direct inspection.

9. Chapter 8. Modeling and Prediction for Processes on Network Graphs

   Eric D. Kolaczyk, Gábor Csárdi

   Abstract

   Throughout this book so far, we have seen numerous examples of network graphs that provide representations—useful for various purposes—of the interaction among elements in a system under study. Often, however, it is some quantity (or attribute) associated with each of the elements that ultimately is of most interest. In such settings it frequently is not unreasonable to expect that this quantity be influenced in an important manner by the interactions among the elements. For example, the behaviors and beliefs of people can be strongly influenced by their social interactions; proteins that are more similar to each other, with respect to their DNA sequence information, often are responsible for the same or related functional roles in a cell; computers more easily accessible to a computer infected with a virus may in turn themselves become more quickly infected; and the relative concentration of species in an environment (e.g., animal species in a forest or chemical species in a vat) can vary over time as a result of the nature of the relationships among species.

10. Chapter 9. Analysis of Network Flow Data

    Eric D. Kolaczyk, Gábor Csárdi

    Abstract

    Many networks serve as conduits—either literally or figuratively—for flows, in the sense that they facilitate the movement of something, such as materials, people, or information. For example, transportation networks (e.g., of highways, railways, and airlines) support flows of commodities and people, communication networks allow for the flow of data, and networks of trade relations among nations reflect the flow of capital. We will generically refer to that of which a flow consists as traffic.

11. Chapter 10. Networked Experiments

    Eric D. Kolaczyk, Gábor Csárdi

    Abstract

    Across the sciences—social, biological, and physical alike—there is a pervasive interest in evaluating the effect of treatments or interventions of various kinds. Generally, the ideal is understood to be to evaluate the proposed treatment in a manner unmarred by bias of any sort. On the other hand, nature and circumstances often conspire to make achievement of this ideal difficult (if not impossible). As a result, there is by now a vast literature on the design, conduct, and analysis of studies for evaluating the efficacy of treatment.

12. Chapter 11. Dynamic Networks

    Eric D. Kolaczyk, Gábor Csárdi

    Abstract

    Most complex systems—and, hence, networks—are dynamic in nature. So, realistically, the corresponding network graphs and processes thereon are dynamic as well and, ideally, should be analyzed as such. Friendships (both traditional and on-line versions) form and dissolve over time. Certain genes may regulate other genes, but only during specific stages of the natural cycle of a cell. And both the physical and logical structure of the Internet have been evolving ever since it was first constructed.

13. Backmatter