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In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices which are connected by edges. A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.
In economics, the Gini coefficient, sometimes called the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income inequality or wealth inequality within a nation or any other group of people. It was developed by the Italian statistician and sociologist Corrado Gini.
Social capital is "the networks of relationships among people who live and work in a particular society, enabling that society to function effectively". It involves the effective functioning of social groups through interpersonal relationships, a shared sense of identity, a shared understanding, shared norms, shared values, trust, cooperation, and reciprocity. Social capital is a measure of the value of resources, both tangible and intangible, and the impact that these relationships have on the resources involved in each relationship, and on larger groups. It is generally seen as a form of capital that produces public goods for a common purpose.
Benchmarking is the practice of comparing business processes and performance metrics to industry bests and best practices from other companies. Dimensions typically measured are quality, time and cost.
Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of nodes and the ties, edges, or links that connect them. Examples of social structures commonly visualized through social network analysis include social media networks, memes spread, information circulation, friendship and acquaintance networks, business networks, knowledge networks, difficult working relationships, social networks, collaboration graphs, kinship, disease transmission, and sexual relationships. These networks are often visualized through sociograms in which nodes are represented as points and ties are represented as lines. These visualizations provide a means of qualitatively assessing networks by varying the visual representation of their nodes and edges to reflect attributes of interest.
A straw poll, straw vote, or straw ballot is an ad hoc or unofficial vote. It is used to show the popular opinion on a certain matter, and can be used to help politicians know the majority opinion and help them decide what to say in order to gain votes.
Governance is all the processes of interaction be they through the laws, norms, power or language of an organized society over a social system. It is done by the government of a state, by a market, or by a network. It is the decision-making among the actors involved in a collective problem that lead to the creation, reinforcement, or reproduction of social norms and institutions". In lay terms, it could be described as the political processes that exist in and between formal institutions.
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease, and brain networks. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin.
Structural cohesion is the sociological conception of a useful formal definition and measure of cohesion in social groups. It is defined as the minimal number of actors in a social network that need to be removed to disconnect the group. It is thus identical to the question of the node connectivity of a given graph. The vertex-cut version of Menger's theorem also proves that the disconnection number is equivalent to a maximally sized group with a network in which every pair of persons has at least this number of separate paths between them. It is also useful to know that k-cohesive graphs are always a subgraph of a k-core, although a k-core is not always k-cohesive. A k-core is simply a subgraph in which all nodes have at least k neighbors but it need not even be connected. The boundaries of structural endogamy in a kinship group are a special case of structural cohesion.
In the study of complex networks, a network is said to have community structure if the nodes of the network can be easily grouped into sets of nodes such that each set of nodes is densely connected internally. In the particular case of non-overlapping community finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But overlapping communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community(ies), and less likely to be connected if they do not share communities. A related but different problem is community search, where the goal is to find a community that a certain vertex belongs to.
The informal organization is the interlocking social structure that governs how people work together in practice. It is the aggregate of norms, personal and professional connections through which work gets done and relationships are built among people who share a common organizational affiliation or cluster of affiliations. It consists of a dynamic set of personal relationships, social networks, communities of common interest, and emotional sources of motivation. The informal organization evolves, and the complex social dynamics of its members also.
In graph theory the conductance of a graph G=(V,E) measures how "well-knit" the graph is: it controls how fast a random walk on G converges to its stationary distribution. The conductance of a graph is often called the Cheeger constant of a graph as the analog of its counterpart in spectral geometry. Since electrical networks are intimately related to random walks with a long history in the usage of the term "conductance", this alternative name helps avoid possible confusion.
Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by nodes and the connections between the elements or actors as links. The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential modeling from statistics, and social structure from sociology. The United States National Research Council defines network science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena."
David Krackhardt is Professor of Organizations at Heinz College and the Tepper School of Business, with courtesy appointments in the Department of Social and Decision Sciences and the Machine Learning Department, all at Carnegie Mellon University in the United States, and he also serves a Fellow of CEDEP, the European Centre for Executive Education, in France. He is notable for being the author of KrackPlot, a network visualization software designed for social network analysis which is widely used in academic research. He is also the founder of the Journal of Social Structure.
In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has a vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of the subgraph's edges. The degeneracy of a graph is the smallest value of k for which it is k-degenerate. The degeneracy of a graph is a measure of how sparse it is, and is within a constant factor of other sparsity measures such as the arboricity of a graph.
Martin Kilduff is a British academic. He is the Professor of Management at the UCL School of Management.
A social network is a social structure made up of a set of social actors, sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for analyzing the structure of whole social entities as well as a variety of theories explaining the patterns observed in these structures. The study of these structures uses social network analysis to identify local and global patterns, locate influential entities, and examine network dynamics.
A simmelian tie is a type of an interpersonal tie, a concept used in the social network analysis. For a simmelian tie to exist, there must be three or more of reciprocal strong ties in a group. A simmelian tie is seen as an even stronger tie than a regular strong tie.
A clique, in the social sciences, is a group of individuals who interact with one another and share similar interests. Interacting with cliques is part of normative social development regardless of gender, ethnicity or popularity. Although cliques are most commonly studied during adolescence and middle childhood development, they exist in all age groups. They are often bound together by shared social characteristics such as ethnicity and socioeconomic status. Examples of common or stereotypical adolescent cliques include athletes, nerds, and "outsiders".
Cognitive social structures (CSS) is the focus of research that investigates how individuals perceive their own social structure. It is part of social network research and uses social network analysis to understand how various factors affect one's cognitive representation of the network. Importantly, an individual's perception of the network may be different than reality. In fact, these differences between the perceived network and the actual network are the focus of many studies that seek insight into how we think about others and our relationships.
References
- Informal networks and organizational crises: An experimental simulation. David Krackhardt, Robert N. Stern - Social Psychology Quarterly, 1988
