# 11: Cliques and Sub-groups

- Page ID
- 7713

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

One of the most common interests of structural analysts is in the "sub-structures" that may be present in a network. The dyads, triads, and ego-centered neighborhoods that we examined earlier can all be though of as sub-structures. In this chapter, we'll consider some approaches to identifying larger groupings.

- 11.1: Introduction to Cliques and Sub-groups
- Network analysts have developed a number of useful definitions and algorithms that identify how larger structures are compounded from smaller ones: cliques, n-cliques, n-clans, and k-plexes all look at networks in this way.

- 11.2: Bottom-up Approaches
- In a sense, all networks are composed of groups (or sub-graphs). When two actors have a tie, they form a "group". One approach to thinking about the group structure of a network begins with this most basic group, and seeks to see how far this kind of close relationship can be extended. This is a useful way of thinking, because sometimes more complex social structures evolve, or emerge, from very simple ones.

- 11.3: Top-down Approaches
- The approaches we've examined to this point start with the dyad, and see if this kind of tight structure can be extended outward. Overall structure of the network is seen as "emerging" from overlaps and couplings of smaller components. Certainly, this is a valid way of thinking about large structures and their component parts. The bottom-up approach may focus our attention on the underlying dynamic processes by which actors build networks.