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Cohesion may be based primarily on interpersonal ties or rely instead on the connection between member and group, while groups may cohere temporarily based on the immediate alignment of interests among members or may be tied together more permanently by socio-emotional bonds. Together, these characteristics define four prototypical group types. Cliques and coalitions are based primarily on dyadic ties. Groups of comrades or colleagues rely instead on the connection of members to the group for cohesion, which reduces the marginal cost of increasing group size. The strong glue of socio-emotional cohesion binds cliques and comrades, while coalitions and groups of colleagues are often based on weaker forms of cohesion. The mix of strong and weak adhesives and the greater scalability offered by the member-group bond provide the building blocks for assembling very large societies without overtaxing the social brain.

This chapter is concerned with maximum degree, clique number, and chromatic number. A focusing (i.e., two-point concentration) phenomenon is demonstrated for the distribution of the maximum degree in the subconnective regime, and likewise for clique number. Laws of large numbers are presented for maximum degree and clique number in the subconnective and connectivity regimes. For the chromatic number, a law of large numbers is presented in the subconnectivity regime, and bounds on its ratio to the clique number are given for the superconnective regime. These bounds are given in terms of packings of the unit ball.

This chapter describes how network analysts define and measure groups. Components are the building blocks of group definitions and consist of all the nodes connected to each other through any number of steps in network. Nodes that cannot reach each other are in different components. More complex group definitions are then provided, namely, k-plexes and n-cliques which permit variation in the degree of connectivity among group members needed to be a group member. The Newman-Girvan (2004) algorithm is introduced which provides mutually exclusive groups and a measure of how well the group definitions characterize the data. The chapter closes with a discussion of how groups influence behavior.

This chapter discusses subgraphs in complex networks. First, it considers ‘building blocks’ of networks-motifs subgraphs that are present in many copies in a network. It focuses on the statistics of cliques and motifs in complex networks. It also discusses ways to detect relatively weakly-interconnected modules in a network (communities) and introduces the notion of modularity.

The author finds that recording children as they engaged in verbal intercourse taught her many things: The author, herself, by trial and error, learned to listen, record, and appreciate the verbal art of children. This is an experience many adults might want to emulate. The recorded child lore conserves a large body of traditional rhymes, songs, taunts, handclaps, and jokes. The child lore also presents new material, much of it gleaned from popular culture. Child lore has expanded over the years to include play aided by technology—phone play, computer play, video games, and reenactments of television and movie scenes. Children on a playground function as a self-governing "people." They make their own rules, and gather in cliques and gangs, which they defend both physically and verbally. Children excel at teaching one another. Children still share verbal lore, despite shorter recesses, endless television watching, and the dominance of computer technology.

This chapter explores the dynamics between the ideal of equality and the reality of significant inequality in the prep school setting. These differences are explored with regard to race, class, international students, day students, form-hierarchy, and cliques. The ways the students negotiate this dichotomy between equality and inequality are part of their gender, class, and ethnic performances.

This chapter discusses the Hindu–Muslim entente and the Lucknow Pact. It looks at the factors that affected the achievement of this entente. It then examines the Bombay session of the All-India Muslim League, which was a very important achievement of Wazir Hasan and Mahmudabad. Here, the discussion shifts to the ‘Lucknow clique’, a group of Muslim politicians who were patronized by the Mahmudabad raja. It then discusses the Lucknow Pact, which was considered a great achievement during the time. Unfortunately, it was unable to meet the goals of its authors, that is, to establish Hindu–Muslim unity. The chapter notes that it was the religious issue of the Ottoman and Khilafat Empire that became the rallying point for Hindu–Muslim unity.

This chapter examines the training camps set up by Dai Li to prepare for the attack of the Japanese armies. It explains that when Dai Li was recalled to Nanjing after the fall of Shanghai, he immediately designated the capital as a special district and put it under the command of Qian Xinmin. It discusses Dai Li's special training unit within the Hangzhou Police Officers Academy and the reorganization of the Juntong which revived the old animosities between the Blue Shirts and the CC clique. It also highlights the creation of the Loyal and Patriotic Army and training unit factionalism.

This chapter examines the fascist principle of the Blue Shirts Society (BSS) in China. It explains that despite the denial of the Goumindang about the existence of BSS, several police reports confirmed that there were individual members of the Fuxingshe and the Chinese Revolutionary Comrades Association (CRCA) who frequently identified themselves as belonging to the Blue Shirts. It discusses Chiang Kai-shek's creation of cliques within the Generalissimo's own power structure and the appointment of brothers Chen Guofu and Chen Lifu as leaders of the so-called CC clique.

This chapter examines ideological rivalries between the Blue Shirts Society and Chiang Kai-shek's CC clique. It explains that by competing with the CC clique for control over the new instruments of print capitalism, the Blue Shirts departed from the brief that they had been given by Chiang Kai-shek to concern themselves mainly with public security and police affairs. It also discusses the expansion of Deng Wenyi's publishing company Give Us a Lift Bookshop into a chain of stores that distributed Chiang loyalists' publications in Nanjing, Hankou, Nanchang, Changsha, Guiyang, and other cities.

This chapter introduces four teens included in this study. They were chosen because their stories are interesting in their own right and because their stories allow the book to introduce important themes and interpretations that are discussed systematically in later chapters. These are Poppy Lopez, a teen who expressed boredom with life in suburbia; Lowanda Smith, a NJ High socialite; Rob Robertson, a community-engaged, intellectually curious, athletically gifted, self-confident, and politically conscious individual; and Kristi Kramer, a teen who did not fit in with any of the cliques in her high school.

This chapter describes techniques for analysing subgraphs in complex networks. It covers the study of network graphlets, motifs, and the use of closed walks to analyse the subgraph structure of a complex network. Analytical expressions for calculating small subgraphs in networks are also given. Then, the chapter introduces the concepts of fragment ratio invariants and studies clustering coefficients, the decay of clustering coefficient with the degree of the nodes, the role of cliques in network clustering, and reciprocity in directed complex networks.

This chapter shows how network theory can improve our understanding of institutional investors’ voting behaviour and, more generally, their role in corporate governance. The standard idea is that institutional investors compete against each other on relative performance and hence might not cast informed votes, due to rational apathy and rational reticence. In other words, institutional investors have incentives to free-ride instead of ‘cooperating’ and casting informed votes. We show that connections of various kinds among institutional investors, whether from formal networks, geographical proximity, or common ownership, and among institutional investors and other agents, such as proxy advisors, contribute to shaping institutional investors’ incentives to vote ‘actively’. They also create intricate competition dynamics: competition takes place not only among institutional investors (and their asset managers) but also at the level of their employees and among ‘cliques’ of institutional investors. Employees, who strive for better jobs, are motivated to obtain more information on portfolio companies than may be strictly justified from their employer institution’s perspective, and to circulate it within their network. Cliques of institutional investors compete against each other. Because there are good reasons to believe that cliques of cooperators outperform cliques of non-cooperators, the network-level competition might increase the incentives of institutional investors to collect information. These dynamics can enhance institutional investors’ engagement in portfolio companies and also shed light on some current policy issues such as the antitrust effects of common ownership and mandatory disclosures of institutional investors’ voting.

We discuss implementation techniques for sparse Gaussian elimination, based on analysis of the sparsity pattern without regard to numerical values. This includes a discussion of data structures for pivot selection, the use of cliques, and the use of both dynamic and static data structures. We examine the division of the solution into the distinct phases of reordering, symbolic factorization, numerical factorization, and solution, indicating the high efficiency with which these steps can now be performed.

This chapter provides a gentle introduction to some modern topics in high-dimensional statistics, statistical learning, and signal processing for an audience who may not have any previous background in these areas. The pedagogical path of the chapter is to first connect recent advances in these fields to the basic topics of statistics, such as estimation, regression, and bias-variance trade-off, as well as to classical—although non-elementary—developments such as sparse estimation and wavelet denoising. After this theoretical introduction, the chapter presents results from more recent research, including discussions on sparse linear regression, the theory of compressed sensing as well as sparse signal reconstruction, approximate message passing, and also sparse and low-rank matrix factorization problems with applications to hidden clique discovery within large networks.

Probabilistic structures on the representations allow for expressing the variation of natural patterns. In this chapter the structure imposed through probabilistic directed graphs is studied. The essential probabilistic structure enforced through the directedness of the graphs is sites are conditionally independent of their nondescendants given their parents. The entropies and combinatorics of these processes are examined as well. Focus is given to the classical Markov chain and the branching process examples to illustrate the fundamentals of variability descriptions through probability and entropy.

First-order logic is a richer language than propositional logic. Its lexicon contains not only the symbols ∧, ∨, ￢, →, and ↔ (and parentheses) from propositional logic, but also the symbols ∃ and ∀ for “there exists” and “for all,” along with various symbols to represent variables, constants, functions, and relations. These symbols are grouped into five categories. • Variables. Lower case letters from the end of the alphabet (… x, y, z) are used to denote variables. Variables represent arbitrary elements of an underlying set. This, in fact, is what “first-order” refers to. Variables that represent sets of elements are called second-order. Second-order logic, discussed in Chapter 9, is distinguished by the inclusion of such variables. • Constants. Lower case letters from the beginning of the alphabet (a, b, c, …) are usually used to denote constants. A constant represents a specific element of an underlying set. • Functions. The lower case letters f, g, and h are commonly used to denote functions. The arguments may be parenthetically listed following the function symbol as f(x1, x2, …, xn). First-order logic has symbols for functions of any number of variables. If f is a function of one, two, or three variables, then it is called unary, binary, or ternary, respectively. In general, a function of n variables is called n-ary and n is referred to as the arity of the function. • Relations. Capital letters, especially P, Q, R, and S, are used to denote relations. As with functions, each relation has an associated arity. We have an infinite number of each of these four types of symbols at our disposal. Since there are only finitely many letters, subscripts are used to accomplish this infinitude. For example, x1, x2, x3, … are often used to denote variables. Of course, we can use any symbol we want in first-order logic. Ascribing the letters of the alphabet in the above manner is a convenient convention. If you turn to a random page in this book and see “R(a, x, y),” you can safely assume that R is a ternary relation, x and y are variables, and a is a constant.

Creativity is usefully viewed from the perspective of personal “worldviews.” which describe the mind as experienced subjectively, from the inside. The worldview of an uncreative person reflects what they’ve been told, while the worldview of a creative person reflects what they’ve done with what they’ve been told to create a self-made worldview. The capacity to generate such a self-made worldview arose first with development of the capacity for one thought to trigger another thought. This chaining allows free-association, critical reflection, or complex behavioural thought sequences to be created and recalled for material with high psychological entropy to be restructured to form a new idea or perspective. However, a second capacity important for creative thought also is needed: contextual focus, the ability to adaptively shift between convergent and divergent modes of thought. Whereas chaining allows the connecting of closely related items in memory, contextual focus enables the forging of distant connections for sophisticated creative expression. Chaining is sufficient for “little-c”, everyday creative ideas, but contextual focus is need for the generation of those “big-C” creative ideas that define major conceptual shifts. These phenomena of mind arise at the level of the brain with coordinated activity of groups of collectively co-spiking neurons (neural cliques). Those that respond to more general or abstract aspects of a situation offer a straightforward mechanism for contextual focus, for example; with associative thought, as more aspects of a situation are taken into account, more neural cliques are recruited. Gabora’s global mind perspective highlights the evolutionary significance of creativity: cultural evolution became possible with the emergence of a creative worldviews that are self-organizing, self-mending, communally interacting, and self-propagating.

This chapter describes the measures and metrics that are used to quantify network structure. The chapter starts with a discussion of centrality measures, which are used to identify central or important nodes in networks. Measures discussed include degree centrality, eigenvector centrality, PageRank, closeness, and betweenness. This is followed by a discussion of groupings of nodes like cliques and components, transitivity measures including the clustering coefficient, structural balance in networks, similarity measures, and assortative mixing.