A graph is, arguably, one of the most ubiquitous mathematical abstractions. Even if you have never encountered this mathematical concept before, you have most likely worked with graphs before. A project plan is a graph; a circuit diagram is a graph; dependencies between files in a software project are graph.

In this book, we shall mostly deal with one type of graph—social graphs or social networks. A social network is simply a collection of sentences that describe relationships, in the following way:

Alice ----likes-----> Bob (noun) (verb) (noun)

The simple phrase above is a basic unit of social network analysis
called a *dyad*. Every dyad denotes a single
relationship—an *edge* in traditional graph theory
(although I use the words *edge* and
*relationship* interchangeably). The nouns in the
phrase represent people involved in the relationship—these are called
*vertices* (plural of *vertex*) or
*nodes* in the mathematical literature (we shall use
*nodes* exclusively).

In social network analysis, nodes have a type. Each node could
represent a person, organization, a blog posting, a hashtag, etc. If a
graph contains nodes of only one type, it’s called a
*1-mode* graph. If it contains relationships between
two types, it’s *bimodal* or
*2-mode*. We can also have multimodal graphs.

We shall start our exploration of social networks with 1-mode graphs—i.e., graphs that link people to people, organizations to organizations, words to words, and so on. We ...

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