core

Examples of core in the following topics:

• Two-mode core-periphery analysis

  • The core-periphery model is indifferent to the density of ties in the off-diagonal blocks.
  • When we apply the core-periphery model to actor-by-actor data (see Network>Core/Periphery), the model seeks to identify a set of actors who have high density of ties among themselves (the core) by sharing many events in common, and another set of actors who have very low density of ties among themselves (the periphery) by having few events in common.
  • Actors in the core are able to coordinate their actions, those in the periphery are not.
  • When we apply the core-periphery model to actor-by-event data (Network>2-Mode>Categorical Core/Periphery) we are seeking the same idealized "image" of a high and a low density block along the main diagonal.
  • So, the "core" is a cluster of frequently co-occurring actors and events.

• K-cores

  • K-cores can be (and usually are) more inclusive than k-plexes.
  • NetDraw includes a tool for identifying and coloring a graph according to its K-cores.
  • The UCINET algorithm for identifying K-cores is located at Network>Regions>K-Core.
  • Each of the seven members of this core has ties to at least three others.
  • The k-core definition is intuitively appealing for some applications.

• World-Systems Theory

  • The United States is an example of a core country -- it has vast amounts of capital and labor is relatively well compensated.
  • They are the buffer between core and peripheral countries.
  • Core countries own most of the world's capital and technology and have great control over world trade and economic agreements.
  • Peripheral countries generally provide labor and materials to core countries.
  • Core countries extract raw materials with little cost.

• Homophily models

  • One way of thinking about this pattern is a "core-periphery" block model.
  • There is a strong form, and a more relaxed form of the core-periphery structure.
  • The Core-periphery 1 model supposes that there is a highly organized core (many ties within the group), but that there are few other ties -- either among members of the periphery, or between members of the core and members of the periphery.
  • Since the "core" is, by definition, the maximally dense area, it appears that the output in version 6.8.5 may be mis-labeled.
  • Core-Periphery 2 offers a more relaxed block model in which the core remains densely tied within itself, but is allowed to have ties with the periphery.

• Global Inequality

  • The world economy is a system divided into a hierarchy of three types of countries: core, semiperipheral, and peripheral.
  • Core countries own most of the world's capital and technology and have great control over world trade and economic agreements.
  • Semiperipheral countries generally provide labor and materials to core countries.
  • Semiperipheral countries exploit peripheral countries, just as core countries exploit both semiperipheral and peripheral countries.
  • Core countries extract raw materials with little cost.

• Node attributes

  • This figure was created by using the Analysis>K-core tool that is built into NetDraw.
  • We'll talk about the precise definition of a k-core in a later chapter.
  • But, generally, a k-core is a set of nodes that are more closely connected to one another than they are to nodes in other k-cores.
  • That is, a k-core is one definition of a "group" or "sub-structure" in a graph.
  • In addition, the size of the nodes in each K-core are proportional to the size of the K-core.

• Preface

  • Our goal in preparing this book is to provide a very basic introduction to the core ideas of social network analysis, and how these ideas are implemented in the methodologies that many social network analysts use.
  • The book is distributed free on the Internet in the hope that it may reach a diverse audience, and that the core ideas and methods of this field may be of interest.

• Thinking Globally

  • In this example, China is the core country, which gathers resources from and sells goods back to Africa, the periphery.
  • This constantly reinforces the dominance of the core countries.
  • Nonetheless, the system is dynamic, and individual states can gain or lose their core (semi-periphery, periphery) status over time.
  • This relationship is exploitative, as the resources needed by peripheral countries to develop are funneled to core countries.
  • Core countries accumulate wealth by gathering resources from and selling goods back to the periphery and semi-periphery.

• Colonialism and Neocolonialism

  • The United States is an example of a core country, with immense capital and relatively high wage labor; Mexico is a semiperipheral country, where the economy has grown rapidly and there is significant technology manufacturing, but where most capital still comes from foreign nations; Liberia is an example of a peripheral country, where virtually all investment is foreign and many wage laborers earn less than $1/day.
  • In this theory, the world economic system is divided into a hierarchy of three types of countries: core, semiperipheral, and peripheral.
  • Core countries (e.g., U.S., Japan, Germany) are dominant capitalist countries characterized by high levels of industrialization and urbanization.
  • Peripheral countries (e.g., most African countries and low income countries in South America) are dependent on core countries for capital, and have very little industrialization and urbanization.
  • Semiperipheral countries (e.g., South Korea, Taiwan, Mexico, Brazil, India, Nigeria, South Africa) are less developed than core nations but are more developed than peripheral nations.

• Study Questions

  • How do K-plexes and K-cores "relax" the definition of a clique?
  • Give an example of when it might be more useful to us a K-plex or K-core approach instead of a strict clique.