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Mathematics LibreTexts

9.1: Introduction

In the previous chapter we looked at the idea of the amount of "embedding" in whole networks - loosely: the extent to which actors find themselves in social structures characterized by dense, reciprocal, transitive, strong ties. The main theme was to understand and index the extent and nature of the pattern of "constraint" on actors that results from the way that they are connected to others. These approaches may tell us some interesting things about the entire population and its sub-populations; but, they don't tell us very much about the opportunities and constraints facing individuals.

If we want to understand variation in the behavior of individuals, we need to take a closer look at their local circumstances. Describing and indexing the variation across individuals in the way they are embedded in "local" social structures is the goal of the analysis of ego networks.

We need some definitions.

"Ego" is an individual "focal" node. A network has as many egos as it has nodes. Egos can be persons, groups, organizations, or whole societies.

"Neighborhood" is the collection of ego and all nodes to whom ego has a connection at some path length. In social network analysis, the "neighborhood" is almost always one-step; that is, it includes only ego and actors that are directly adjacent. The neighborhood also includes all of the ties among all of the actors to whom ego has a direct connection. The boundaries of ego networks are defined in terms of neighborhoods.

"N-step neighborhood" expands the definition of the size of ego's neighborhood by including all nodes to whom ego has a connection at a path length of N, and all the connections among all of these actors. Neighborhoods of greater path length than 1 (i.e. ego's adjacent nodes) are rarely used in social network analysis. When we use the term neighborhood here, we mean the one-step neighborhood.

"In" and "Out" are other kinds of neighborhoods. Most of the analysis of ego networks uses simple graphs (i.e. graphs that are symmetric, and show only connection/not, not direction). If we are working with a directed graph, it is possible to define different kinds of ego-neighborhoods. An "out" neighborhood would include all the actors to whom ties are directed from ego. An "in" neighborhood would include all the actors who sent ties directly to ego. We might want to define a neighborhood of only those actors to whom ego had reciprocated ties. There isn't a single "right" way to define an ego neighborhood for every research question.

Most analysis of ego networks uses binary data - two actors are connected or they aren't, and this defines the ego neighborhood. But if we have measured the strength of the relation between two actors, and even its valence (positive or negative), we need to make choices about when we are going to decide that another actor is ego's neighbor. With ties that are measured as strengths or probabilities, a reasonable approach is to define a cut-off value (or, better, explore several reasonable alternatives). This reasoning is the origin of strong tie neighborhoods and weak tie neighborhoods. Where the information about ties includes information about positive/negative, the most common approach is to analyze the positive tie neighborhood and the negative tie neighborhood separately.