Chapter 4
Modelling relationships
of different types
Our first use of the layer approach is to model relationships that are of qualitatively
different kinds, such as the examples of friends and colleagues that we have already
mentioned. There are, of course, many different possible relationships: not only
friends and colleagues, but close family members, more distant family members,
school and university friends, fellow members of interest groups, and professional
contacts. These different kinds of relationships have different properties. As the
simplest example, not all of the facts about an individual’s life would necessarily
be appropriate to share with everyone that individual has a relationship with. As
a result, the property of influence would operate differently along some edges than
others because of the kind of information that could/should traverse them.
As we have indicated, our approach will be to use a layer for each kind of
relationship. So there might be a friends layer, a family layer, a colleagues layer,
and so on. There is no difficulty allowing any edge to have an associated weight,
reflecting the intensity of that relationship. Note, however, that these weights have
to be on the same scale, no matter what kind of relationship they are associated with.
For example, it might be natural that family edges have weights that are, on average,
larger than those of colleague edges. To simplify the exposition, we will think of
the different edge types as being labelled with different colors. These colors can be
mapped to any set of relationship types.
The payoff from modelling a social network with typed edges is that we can
determine the structure of the complete ecosystem of individuals with all of their
multiple relationship types. We can also measure the social distance between any
pair of individuals, taking into account all of the ways in which they are connected,
directly and indirectly.
Ignoring the different kinds associated with the relationships — taking the
monochrome view of the social network — loses information about the ways in
which humans relate to one another. In particular, the social network will seem
smaller than it should be; individuals will seem more similar than they “should”.
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Modelling relationships
of different types
Our first use of the layer approach is to model relationships that are of qualitatively
different kinds, such as the examples of friends and colleagues that we have already
mentioned. There are, of course, many different possible relationships: not only
friends and colleagues, but close family members, more distant family members,
school and university friends, fellow members of interest groups, and professional
contacts. These different kinds of relationships have different properties. As the
simplest example, not all of the facts about an individual’s life would necessarily
be appropriate to share with everyone that individual has a relationship with. As
a result, the property of influence would operate differently along some edges than
others because of the kind of information that could/should traverse them.
As we have indicated, our approach will be to use a layer for each kind of
relationship. So there might be a friends layer, a family layer, a colleagues layer,
and so on. There is no difficulty allowing any edge to have an associated weight,
reflecting the intensity of that relationship. Note, however, that these weights have
to be on the same scale, no matter what kind of relationship they are associated with.
For example, it might be natural that family edges have weights that are, on average,
larger than those of colleague edges. To simplify the exposition, we will think of
the different edge types as being labelled with different colors. These colors can be
mapped to any set of relationship types.
The payoff from modelling a social network with typed edges is that we can
determine the structure of the complete ecosystem of individuals with all of their
multiple relationship types. We can also measure the social distance between any
pair of individuals, taking into account all of the ways in which they are connected,
directly and indirectly.
Ignoring the different kinds associated with the relationships — taking the
monochrome view of the social network — loses information about the ways in
which humans relate to one another. In particular, the social network will seem
smaller than it should be; individuals will seem more similar than they “should”.
31