Tore Opsahl

Thesis: 1 Introduction

As we move toward a highly competitive global economy where no person or firm acts in isolation (Drucker, 1993; Harris, 2001), it is vital to understand the systems in which people and firms interact. These systems can be represented as networks where the entities are called nodes and interactions among them are represented in terms of ties. More generally, a node can be a neuron, an individual, a group, an organisation, or even a country, whereas ties can take the form of friendship, communication, collaboration, alliance, or trade, to name only a few (Wasserman and Faust, 1994). For example, within an organisation, the network of social interactions among employees has been referred to as the organisation’s informal structure (Hinds and Kiesler, 1995). This informal structure can reflect particular aspects of social interaction. For instance, a possible informal structure is the advice network within an organisation. The ties in this network are formed when an employee asks another for advice (Lazega, 2001). Another intra-organisational network is the one that maps the collaboration structure among employees (Cross and Parker, 2004). In this case, ties would be formed between employees collaborating on projects or other work-related tasks.

Many research problems within a wide range of disciplines can be framed within a network perspective (Wasserman and Faust, 1994; Watts, 2004). This has led to the development of social network analysis in sociology (Freeman, 2004), the analysis of complex networks in physics (Newman, 2003), and graph theory in mathematics and computer science (Bollobas, 1998; Leskovec et al., 2005). This research has been both theoretical (Erdoos and Renyi, 1960; Granovetter, 1973; Heider, 1946; Luce and Perry, 1949) and empirical (Bernard et al., 1988; Foster et al., 1963; Milgram, 1967; Moreno, 1938; Watts and Strogatz, 1998). Stanley Milgram (1967) and his colleagues (Korte and Milgram, 1970; Travers and Milgram, 1969) conducted one of the first empirical studies on the structure of social networks and the average shortest distance between nodes (i.e., the lowest number of ties that directly (distance = 1) or indirectly (distance ≥ 1) separate nodes). He randomly chose people from a phone directory in Nebraska, a state located in the Midwestern United States. Each person was asked to send a letter to someone whom they knew on a first-name basis with the goal of ultimately reaching a stockbroker in Boston. The best strategy for the people was to send the letter to someone whom they perceived to be either socially or geographically closer to the stockbroker in some sense. A number of Milgram’s letters did reach the stockbroker, and the average number of people that those letters had passed through was only about six. There were weaknesses and biases in Milgram’s research. For example, letters which passed through more people were perhaps more likely to get lost or forgotten, or there might have been shorter paths for the letters to travel than the ones that were recorded. Nonetheless, Milgram’s “six-degrees-of-separation” experiment is usually taken as evidence of the “small-world” effect (Watts and Strogatz, 1998). This effect refers to the fact that a short distance separates most people, even when the size of the population is very large and when people have a tendency to form small tightly knit groups. Milgram’s research does not address the reasons why certain letters reached the stockbroker while others got lost, and the features of the network that impacted on this. A critical review of this work can be found in Wasserman and Faust (1994) and Watts (1999).

In addition to studying the shortest paths that connect nodes, a substantial body of work has concentrated on other features of networks (e.g., Bernard et al., 1988; Fararo and Sunshine, 1964; Foster et al., 1963). To this end, a number of complete social networks (i.e., networks for which information on a specific set of nodes and all ties among them is available) have been collected with a view to uncovering the global structural patterns that emerge from the ways in which individuals behave at a local level. Among the early empirical studies are the studies by Foster et al. (1963) and Fararo and Sunshine (1964), who constructed maps of friendship networks among high-school students, and by Bernard et al. (1988) who did the same for communities of Utah Mormons, Native Americans, and Micronesian islanders. These efforts have been variously motivated. For example, some were aimed at bettering our understanding of human interaction patterns (Bernard et al., 1988; Fararo and Sunshine, 1964; Holland and Leinhardt, 1971; Lazarsfeld and Merton, 1954; Wasserman and Pattison, 1996); others focused on the spread of information and infectious diseases (Valente, 1995), and the effect of network on individuals’ and organisations’ performance (Burt, 1992; Coleman, 1988; Gulati and Gargiulo, 1999). More generally, scholars have been interested in the mechanisms governing tie generation and network evolution (Holland and Leinhardt, 1981; Powell et al., 2005; Snijders, 2001; Wasserman and Pattison, 1996). Early studies have investigated how people may benefit from participating in small dense groups (Coleman, 1988; Heider, 1946), for example by choosing new acquaintances that are already tied to current acquaintances, a process known as triadic closure (Davis, 1970; Heider, 1946; Holland and Leinhardt, 1970). In addition, a longstanding tradition of research has focussed on the effect that sharing demographic characteristics has on the existence of a tie (Lazarsfeld and Merton, 1954), and the term homophily was coined to indicate the tendency of individuals to interact with others socially similar to themselves (for a review, see McPherson et al., 2001). Scholars have also been concerned with the effects of focus constraints on tie generation, and empirically examined the tendency of social relationships to be established preferentially between individuals that share activities, roles, and social positions (Feld, 1981; Monge et al., 1985).

While directly probing the network structure and functioning, many of the early empirical studies of social networks suffered from two fundamental weaknesses. These weaknesses stem from the data collections methods that were typically used to record social interactions, namely interviews and surveys (for a review, see Marsden, 1990). First, the methods were sensitive to subjective bias on the part of interviewees. In particular, what is considered an “acquaintance” or a “friend” can differ considerably from one person to another. This bias is usually referred to as the informant inaccuracy bias (Bernard et al., 1984). Second, survey instruments and direct observation methods are typically labour-intensive and onerous to administer. Thus, the number of nodes in the collected network is limited. In fact, the early social networks often comprised only a few tens (e.g., Bernard et al., 1988) or hundreds (e.g., Fararo and Sunshine, 1964) of people. An implication of the small network size is that it is difficult to perform robust statistical analysis, which in turn easily could result in biased conclusions.

To overcome these shortcomings, a number of researchers have studied networks for which there exist more precise definitions of connectedness (Watts and Strogatz, 1998), and collected much larger network datasets using archival records (Burt and Lin, 1977). Examples of such networks are the neural network of worms (Watts and Strogatz, 1998), electric power grid (Watts and Strogatz, 1998), the Internet (Albert et al., 1999; Broder et al., 2000), and the pattern of air traffic between airports (Amaral et al., 2000; Barrat et al., 2004). However, these networks suffer from a different problem: although they may loosely be regarded as social networks in the sense that their structure in some way reflects features of the society in which they are embedded, they do not measure actual ties among people. Many researchers are, of course, interested in these networks for their own sake, but to the extent that we want to find out more about individuals’ interaction patterns, neural networks of worms, power grids, and computer networks are a poor substitute for the real thing.

In recent years, however, two considerable developments have prompted noteworthy advances in social network analysis. First, to explore patterns of interactions among individuals in large-scale networks, Watts and Strogatz (1998) investigated the network of movie actors and Uzzi and Spiro (2005) studied the network of the artists working in Broadway musicals. In these networks, which has been meticulously constructed from archival data and contains thousands of people, two people are considered connected if they have been credited with appearance in the same movie or musical. In addition, a number of authors have studied scientists collaborating on patents and scientific publications (Barabasi et al., 2002; Hall et al., 2001; Moody, 2004; Newman, 2001d). In these networks, some of which contain millions of scientists, a tie is considered to exist between two scientists if they have worked on a patent or paper together. However, while all these network are indeed made of people, they are not without limitations. A major weakness is the validity of ties. In other words, the appearance of two actors in the same movie or collaboration of two scientists on a publication does not necessarily imply that they are acquainted in any, but the most cursory fashion, or that their social relationship extends beyond the artistic or scientific endeavour. Furthermore, in co-authorship networks, the network structure can be biased by the fact that some scientists are listed as authors on an extremely large number of papers. This might be due to the common practice of some research institutes to list the directors’ names on most of the papers published by scientists at these institutes (Newman, 2001d). These scientists have not necessarily interacted with all the other scientists they have co-authored with; however, they are likely to act as hubs by creating shortcuts among different groups of nodes, and thereby reduce the distance among nodes in the overall network.

Second, a remarkable deterioration of boundaries between disciplines has been responsible for new theoretical developments and a variety of new analytical tools for modelling the structure and behaviour of networks. Previously, on the one hand, social and behavioural scientists studied in-depth social relationships, whereas, on the other, physicists and applied mathematicians developed methods for analysing large-scale networks. However, through interdisciplinary collaborations, these two sides have been brought together. In fact, Chapter 3 of this thesis is the outcome of a collaboration among social scientists and physicists. These two advances have contributed to the birth of what has been called the “new science of networks” (Watts, 2004).