Network Analysis
Network Analysis
Network analysis is a cluster of methodological techniques for the mathematical description and investigation of networks. It has applications across both the natural and the social sciences. Electronic networks, river networks, etymological networks, epidemiological networks, and networks of economic transactions have all been subjects for network analysis. In the social sciences, the concern is with the investigation of social networks. A social network is any articulated pattern of connections in the social relations of individuals, groups, and other collectivities. Social networks include friendship and kinship networks, interorganizational networks, communication networks, scientific citation networks, and policymaker networks. Social network analysis, then, deals with relational data in all areas of social life. It handles the contacts, ties, and connections, group attachments, and meetings that relate one person or group to another and that cannot be reduced to the properties of the individual agents themselves. Such relational data are central to the building of models of the structures through which action is organized. Social network analysis is not limited to small-scale and interpersonal structures, and there have been many applications to such phenomena as global trading relations in world systems.
Social network analysis developed independently in the social anthropology of small societies and the social psychology of small groups. Anthropologists such as Alfred Radcliffe-Brown (1881–1955) pioneered a view of social structure as a “web” of social relations and an idea of actions “interweaving” and “interlocking” through such a network of connections. Anthropologists in this tradition began to investigate the “density” of these social networks and the “centrality” of individuals within them. Small group researchers in the Gestalt tradition developed ways of investigating the pattern of relations within the “life space” of social groups, the most influential example of this being Jacob Moreno’s (1892–1974) sociometric studies of schoolroom friendship choices. The study of “group dynamics” developed rapidly from the 1950s with more formal applications of the network idea.
Contemporary network analysis grew markedly from the early 1970s, when a group of students and researchers working with Harrison White began to explore the use of more formal mathematical models for the analysis of small group and anthropological data and began to extend these investigations to wider sociological phenomena. A landmark study from this burgeoning work was Mark Granovetter’s Getting a Job (1974). Granovetter showed that people’s chances of getting information about job opportunities depended not on the formal methods of job search that they used but on their location in informal social networks. Counterintuitively, he also showed that having a small number of “weak” ties was far more important than having many “strong” ties: information came from “acquaintances” rather than close “friends” and relatives. This group of researchers used algebraic models from set theory and ideas from the mathematical theory of graphs, along with methods of multidimensional scaling. Together, this cluster of methods established a framework of network analysis that spread rapidly across sociology and into the other social sciences.
The basic idea in social network analysis is that a social network can be modeled as a set of “points” connected by “lines,” the points representing the individuals and groups, and the lines representing their social relations. The simplest applications involve drawing a graph of points and lines to represent a social network and then visually examining the pattern of lines for its structural properties. When dealing with more than a small number of points, however, more abstract methods are necessary, and the mathematical methods allow the points and lines to be recorded in a matrix ready for mathematical processing. This has allowed the investigation of such structural properties as the density of relations, the centrality of agents, the formation of cliques and components, and the assessment of social distance. A measure of density, for example, assesses the proportion of all possible relations that actually exist in a network and is an important indicator of solidarity and cohesion. Cliques are subnetworks into which networks may be divided and that may comprise groups capable of independent action. Centrality concerns the strategic positions that actors may hold in the overall pattern of connections and the consequent flow of influence, support, or power.
Important applications of network analysis have been undertaken in many areas of the social sciences. Claude Fischer (1982) and Barry Wellman (1979) investigated community networks in cities with high levels of geographical mobility, and they explored the increasing reliance that people have placed on electronic methods and virtual channels of communication for maintaining interpersonal cohesion. The work of Robert Putnam was influential in advocating the idea that people’s networks of social relations could be regarded as forms of social capital. This view has been elaborated in the competing approaches of Nan Lin (2001) and Ron Burt (2005). Lin stresses individual investments in social relations and the rational actions that are involved in the accumulation of social capital. Burt has looked at processes of brokerage and social closure—rooted in measures of centrality and prominence—for the creation of social capital.
Jim Bearden and various coworkers have explored structures of interlocking directorships in business, examining the nature and significance of bank centrality within financial networks (Mintz and Schwartz 1985). David Knoke has pioneered methods for studying networks of political connection and influence, leading to numerous studies of policy networks and the role of power in the policy process (Knoke et al. 1996). Peter Bearman (1993) is one of a number of researchers who has demonstrated the uses of network analysis for historical data on stratification and power relations. Many important studies have been undertaken on organizational networks in business, and these have been extended into work on knowledge management by Rob Cross (Cross and Parker 2004) and David Snowden (Kurtz and Snowden 2005). Important methodological work includes that of Linton Freeman on approaches to network visualization, using methods of pictorial display for the analysis of large social networks. These have been used in his own study of the development of social network analysis (Freeman 2004).
Applications of social network analysis have tended to be both descriptive and static, leading many to ask whether network analysts are doing anything more than producing pretty pictures and arbitrary numbers. This has been reinforced by the incursions of many physicists into the area of network analysis. These physicists have argued—often in ignorance of what work has actually been undertaken by social network analysts—that their methods have far more to offer in the analysis of social relations (Watts 2003). What is clear, however, is that these discussions have begun to shift social network analysis toward a greater concern for explanation, rather than simply description, and toward the investigation of dynamic processes in social networks.
The need to combine network analysis with agent-level models has been emphasized by Mustafa Emirbayer and his colleagues (Emirbayer 1997; Emirbayer and Goodwin 1994), who stress the interdependence of cultural, structural, and agency analyses. Network analysis must be combined with an awareness of the culturally formed subjective motivations and commitments of actors, whose intentional actions produce, reproduce, and transform network structures. This model of the structuration of social networks stresses the iterative nature of rule-governed actions. This is echoed in the growth of agent-based computational methods of network analysis that propose ways of linking microlevel decision making with macrolevel structural change (Monge and Contractor 2003).
SEE ALSO Networks
BIBLIOGRAPHY
Bearman, Peter. 1993. Relations into Rhetorics: Local Elite Social Structure in Norfolk, England, 1540–1640. New Brunswick, NJ: Rutgers University Press.
Burt, Ronald S. 2005. Brokerage and Closure: An Introduction to Social Capital. New York: Oxford University Press.
Carrington, Peter J., John Scott, and Stanley Wasserman, eds. 2005. Models and Methods in Social Network Analysis. New York: Cambridge University Press.
Cross, Rob, and Andrew Parker. 2004. The Hidden Power of Social Networks: Understanding How Work Really Gets Done in Organizations. Cambridge, MA: Harvard Business School Press.
Emirbayer, Mustafa. 1997. Manifesto for a Relational Sociology. American Journal of Sociology 103 (2): 281–317.
Emirbayer, Mustafa, and Jeff Goodwin. 1994. Network Analysis, Culture, and the Problem of Agency. American Journal of Sociology 99 (6): 1411–1454.
Fischer, Claude S. 1982. To Dwell Among Friends: Personal Networks in Town and City. Chicago: Chicago University Press.
Freeman, Linton S. 2004. The Development of Social Network Analysis: A Study in the Sociology of Science. Vancouver, BC: Empirical Press.
Granovetter, Mark. 1974. Getting a Job: A Study of Contacts and Careers. Cambridge, MA: Harvard University Press. 2nd ed. 1995. Chicago: University of Chicago Press.
Knoke, David, Franz U. Pappi, Jeffrey Broadbent, and Youtaka Tsujinaka. 1996. Comparing Policy Networks: Labor Politics in the U.S., Germany, and Japan. New York: Cambridge University Press.
Kurtz, Cynthia F., and David J. Snowden. 2005. The New Dynamics of Strategy: Sense-making in a Complex and Complicated World. IBM Systems Journal 42 (3): 462–483.
Lin, Nan. 2001. Social Capital: A Theory of Social Structure and Action. Cambridge, U.K.: Cambridge University Press.
Mintz, Beth, and Michael Schwartz. 1985. The Power Structure of American Business. Chicago: University of Chicago Press.
Monge, Peter R., and Noshir Contractor. 2003. Theories of Communication Networks. New York: Oxford University Press.
Scott, John. 2000. Social Network Analysis: A Handbook. 2nd ed. London: Sage.
Scott, John. 2002. Social Networks: Critical Concepts in Sociology. 4 vols. London: Routledge.
Wasserman, Stanley, and Katherine Faust. 1994. Social Network Analysis: Methods and Applications. New York: Cambridge University Press.
Watts, Duncan J. 2003. Six Degrees: The Science of a Connected Age. New York: Norton.
Wellman, Barry. 1979. The Community Question: The Intimate Networks of East Yorkers. American Journal of Sociology 84: 1201–1231.
Wellman, Barry, and Stephen D. Berkowitz, eds. 1988. Social Structures: A Network Approach. Cambridge, U.K.: Cambridge University Press.
John Scott
Network Topologies
Network Topologies
The topology of a network is the geometric representation of all links and nodes of a network—the structure, consisting of transmission links and processing nodes, that provides communications connectivity between nodes in a network. A link is the physical transmission path that transfers data from one device to another. A node is a network addressable device.
Graph theory describes certain characteristics of a network topology such as the average node degree for robustness (average number of links terminating at a node in a network), network diameter for size (the longest/shortest path between any two nodes in a network), number of paths for complexity (total number of paths between all node pairs), and cutsets for flow (minimum number of removed links to partition a network). However, the most dominant characteristic of a network topology is its shape.
Mesh, Star, Tree, Bus, Ring
The most general shape characteristics are symmetry and regular/irregular shape. There are five basic network topology regular shapes: mesh, star, tree, bus, and ring. The bus is a special case of a tree with only one trunk. The mesh has the highest node degree; the bus has the lowest node degree.
Mesh Topology.
In a mesh topology, every node has a dedicated point-to-point link to every other node which requires n(n–1)/2 links to connect n nodes. This is the original way the telephone network started in major East Coast U.S. cities. Before long the sky was not visible on certain downtown intersections due to the amount of overhead wire! The mesh topology allows for robustness in presence of faults since the loss of links or nodes can be routed around due to the amount of connectivity. However, this comes at the cost of complex network management due to the number of links and expensive resource usage since each n node must have n–1 ports to connect in the mesh.
Star Topology.
In a star topology, each node has a dedicated point-to-point link to a central hub. If one node wants to send data to another, it sends to the central hub, which then relays the data to the destination node. A star provides centralized control but also represents a performance bottleneck and single-point-of-failure.
Tree Topology.
A tree topology occurs when multiple star topologies are connected together such that not every node is directly connected to a central hub. Thus, a tree extends a star topology, allowing for community clustering around local hubs. The two fundamental trees upon which topologies are built are: the minimum spanning tree, which is the least-cost tree connecting all nodes in a graph; and the Steiner Tree (ST), which is the least-cost tree connecting a subset of member nodes in a graph. (The ST may contain non-member nodes also, which are called Steiner points). Cost is determined by placing weights on links and nodes based on predetermined metrics such as distance, supply/demand, economic cost, delay, or bandwidth .
Bus Topology.
In a bus topology, a shared medium connects all nodes in the network. This shared medium may be a single wire or radio frequency. The shared medium provides ease-of-installation and flexibility, since it initially consists of a single cable run alongside targeted computers or computers broadcasting on specific frequencies. However, the shared medium also creates two problems: collisions when two nodes broadcast simultaneously, and fault management, since any network problems affect all connected computers. Isolating the problem requires physically separating the shared medium in a methodological manner.
Ring Topology.
The ring topology is a series of unidirectional, dedicated point-to-point links connecting in a physical ring. This topology provides inherent reliability since a signal from a source travels around the ring to the destination and back to the source as an acknowledgement. Least-cost rings may approach the cost of a least-cost tree but are generally more expensive and have more delay. Also a ring is not a flexible topology—adding and deleting links and nodes is disruptive.
Usage Tradeoffs
Protocols are matched to these topologies to enable computer network usage. The bus topology requires a shared medium access protocol based on sensing transmission to avoid collisions with probabilistic retransmission (that is, retransmission after a probabilistically determined time). The ring topology requires a token-passing where a node needs to have a token in order to transmit. At high loads, the bus topology with a shared medium access protocol experiences collisions, and thus offers diminished performance beyond a particular usage threshold. The ring topology with a token-passing protocol has unnecessary overhead at low loads but its performance does not degrade at high loads.
In general, there are two alternatives for operation of a star: (1) the central hub broadcasts all traffic it receives (physically a star but logically a bus), or (2) the central hub selectively switches incoming traffic only to destination nodes. The performance of a star depends on the processing capability of the central hub as well as the capacity of the spoke links, and beyond a threshold connections may be blocked. The tree topology is used for multipoint or group communications and thus depends on the slowest link or node with lowest processing capability in the tree connecting the group.
Examples
Examples of networks matched to these topologies include local area network (LAN) standard ETHERNET, which is a bus topology using a shared media access protocol, and LAN standard TOKEN RING, which is a ring topology using a token-passing protocol. The star is the topology of the local loop, circuit-switched telephone network with the central hub being the local central office. The tree topology is the basis of emerging group communication applications that are not yet standardized.
see also Bridging Devices; Internet; Network Design; Network Protocols; Office Automation Systems; Telecommunications.
William J. Yurcik
Bibliography
Stallings, William. Data and Computer Communications, 6th ed. Upper Saddle River, NJ: Prentice Hall, 2000.
network architecture
Interconnection topology is also considered a part of network architecture. There are three generic forms of topology: star, ring, and bus. Star topology consists of a single hub node with various terminal nodes connected to the hub; terminal nodes do not interconnect directly. By treating one terminal node as the hub of another star, a treelike topology is obtained. In ring topology all nodes are on a ring and communication is generally in one direction around the ring; some ring architectures use two rings, with communication in opposite directions. Various techniques (including time division multiplexing, token passing, and ring stretching) are used to control who is allowed to transmit onto the ring. Bus topology is noncyclic, with all nodes connected; traffic consequently travels in both directions, and some kind of arbitration is needed to determine which terminal can use the bus at any one time; Ethernet is an example. Hybrids that mix star and ring topologies have been employed.
A special area of network architecture is involved with the necessary disciplines required of some of the newer network architectures (see ring network, token ring, Ethernet).