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Chapter 2. The core model
There are three sets of distances that inform us about the social network. The
lengths of the solid edges tell us how close any two individuals are as colleagues.
The dashed edges tell us how close any two individuals are as friends. Suppose
that individual A has friend B who has colleague C who has friend D. The distance
between the friend version of A and the friend version of D tells us how similar A
and D are likely to be as friends in the context of this entire social network. The
key benefit of analyzing the social network in this combined way is that it takes into
account the colleague similarity of B and C (as well as any friendship between them)
in estimating the relationship between A and D. Analyzing the social network of
friends and the social network of colleagues separately does not take into account
the existence of these combined relationship chains.
We can also estimate how strong the relationship between A and D might be as
colleagues by considering the distance between the colleague versions of their nodes
in the embedding. The strength of a friend relationship and a colleague relationship
between the same two individuals need not, of course, be similar.
When two nodes from the same layer are embedded close to one another, but
there is no edge between them in the social network, this signals that, in some sense,
there ought to be such an edge. The similarity of their positions in the embedding
occurs because they see the rest of the social network in a similar way. This observation is the foundation for edge prediction, detecting pairs of nodes for which a
relationship is (somehow) missing. In some contexts, this might indicate a problem
with data collection; in others, it suggests that there is a potential relationship that
can be suggested to both individuals. Social media platforms use this as the basis of
suggesting “people you may know”.
Using our typed-edge approach, such recommendations can be enriched because we are in a position to suggest what kind of relationship might or should exist.
Thus the recommendation could be “this is someone who might be a potential colleague” or “this is someone who might be a potential friend”. There are obvious
commercial possibilities to this finer level of recommendation.
The lengths of the vertical edges also have two useful interpretations:
1. A long embedded edge indicates a dissonance between the roles played by the
node in the different (sub)social networks that each layer represents. For example, if the red layer represents work colleagues, and the green layer friends,
then the vertical edges represent the internal effort an individual requires to
“change hats”, for example, to remember to pass on some news or a joke
heard at work to a friend. A long edge reveals the fact that there are significant
differences between the role that the individual plays in the work-based social
network, and the role played in the friend-based social network.
2. In settings where the edges represent properties that have flow associated with
them, the length of embedded vertical edges more directly signals the amount
of resistance to such flows. For example, the edges might represent influence.
A short vertical edge signals little resistance, and so strong influence, internally
from one role to the other. An individual with a short vertical edge in the
embedding is someone who forms a good bridge for information or influence
Chapter 2. The core model
There are three sets of distances that inform us about the social network. The
lengths of the solid edges tell us how close any two individuals are as colleagues.
The dashed edges tell us how close any two individuals are as friends. Suppose
that individual A has friend B who has colleague C who has friend D. The distance
between the friend version of A and the friend version of D tells us how similar A
and D are likely to be as friends in the context of this entire social network. The
key benefit of analyzing the social network in this combined way is that it takes into
account the colleague similarity of B and C (as well as any friendship between them)
in estimating the relationship between A and D. Analyzing the social network of
friends and the social network of colleagues separately does not take into account
the existence of these combined relationship chains.
We can also estimate how strong the relationship between A and D might be as
colleagues by considering the distance between the colleague versions of their nodes
in the embedding. The strength of a friend relationship and a colleague relationship
between the same two individuals need not, of course, be similar.
When two nodes from the same layer are embedded close to one another, but
there is no edge between them in the social network, this signals that, in some sense,
there ought to be such an edge. The similarity of their positions in the embedding
occurs because they see the rest of the social network in a similar way. This observation is the foundation for edge prediction, detecting pairs of nodes for which a
relationship is (somehow) missing. In some contexts, this might indicate a problem
with data collection; in others, it suggests that there is a potential relationship that
can be suggested to both individuals. Social media platforms use this as the basis of
suggesting “people you may know”.
Using our typed-edge approach, such recommendations can be enriched because we are in a position to suggest what kind of relationship might or should exist.
Thus the recommendation could be “this is someone who might be a potential colleague” or “this is someone who might be a potential friend”. There are obvious
commercial possibilities to this finer level of recommendation.
The lengths of the vertical edges also have two useful interpretations:
1. A long embedded edge indicates a dissonance between the roles played by the
node in the different (sub)social networks that each layer represents. For example, if the red layer represents work colleagues, and the green layer friends,
then the vertical edges represent the internal effort an individual requires to
“change hats”, for example, to remember to pass on some news or a joke
heard at work to a friend. A long edge reveals the fact that there are significant
differences between the role that the individual plays in the work-based social
network, and the role played in the friend-based social network.
2. In settings where the edges represent properties that have flow associated with
them, the length of embedded vertical edges more directly signals the amount
of resistance to such flows. For example, the edges might represent influence.
A short vertical edge signals little resistance, and so strong influence, internally
from one role to the other. An individual with a short vertical edge in the
embedding is someone who forms a good bridge for information or influence