Scale-Free Network

Compare Random Network and the “Scale-Free” Network Proposed by Barabási and Albert

Abstract

Network theory has recently gained importance as an interdisciplinary approach for understanding complex systems. With roots in the physical sciences and sociology, scholars have identified common features of networks in diverse physical and social settings. Despite considerable interest in political networks, especially transnational advocacy networks (TANs), political scientists have imported few insights from network theory into their studies. Nor have political scientists apparently exported their insights and knowledge of political processes to network theory. This essay aims to begin an exchange between network theorists and political scientists by addressing two related questions. Conversely, what problems arise in political phenomena that can enrich network theory?

In network theory, networks are typically treated as varying along three related dimensions: 1) the number of nodes; 2) the density of the network or the frequency of interactions between nodes; and 3) the structure of the network, defined as the pattern of connections between nodes. In turn, these dimensions, and especially structure, have been used to analyze and explain the efficiency and robustness of different networks. Efficiency is the ability to transmit information across the network “quickly,” with speed defined as the number of links between nodes through which a message must travel before reaching its target. Robustness, by contrast, is the ability of the network to function (i.e., transmit information) after the “failure” of a node or its removal from the network (Barabasi 2003, 111-122). Networks, then, are defined as a set of interconnections between nodes, differentiated by the quality and quantity of connections.

Random Network and the “Scale-Free” Network Proposed by Barabási and Albert

Introduction

We are surrounded by complex systems, from cells made of thousands of molecules to society, a collection of billions of interacting individuals. These systems display signatures of order and self-organization. Understanding and quantifying this complexity is a grand challenge for science. Kinetic theory demonstrated at the end of the nineteenth century that the measurable properties of gases, from pressure to temperature, can be reduced to the random motion of atoms and molecules. In the 1960s and 70s, researchers developed systematic approaches to quantifying the transition from disorder to order in material systems such as magnets and liquids. Chaos theory dominated the quest to understand complex behavior in the 1980s with the message that complex and unpredictable behavior can emerge from the nonlinear interactions of a few components. The 1990s was the decade of fractals, quantifying the geometry of patterns emerging in self-organized systems, from leaves to snowflakes (Albert, 2002, pp. 47-97).

Despite these conceptual advances, a complete theory of complexity does not yet exist. When trying to characterize complex systems, the available tools fail for various reasons. First, most complex systems are not made of identical components, such as gases and magnets. Rather, each gene in a cell or each individual in society has its own characteristic behavior. Second, while the interactions among the components are manifestly nonlinear, truly chaotic behavior is more the exception than the ...