Chapter 7
Modelling relationships
that change over time
So far, all of our social networks have assumed that relationships are static: they
either exist or not between any pairs of nodes, and intensities, as described by edge
weights, do not change. This is not very realistic. Relationships are created (and
sometimes lapse), and the intensity of any particular relationship ebbs and flows
over time. It is useful to be able to model the effect of each of these changes on
the overall structure of the social network, and so we turn our attention to modelling
edges whose intensities change with time. We include in this edges that may come
into existence (that is, a change from an intensity of zero to a non-zero value), and
that disappear (that is, a change from a non-zero intensity to an intensity of zero).
7.1 Temporal networks
Temporal (dynamic) social network analysis aims to understand the structures in networks as they evolve, building on static analysis techniques but adding a mechanism
for variation with time.
The benefits, and drawbacks, of graph representations of relationships is that
a single change, for example the addition or deletion of an edge, can change the
entire graph structure. When a social network changes from one time to another,
reflecting this change completely requires a fresh embedding of the graph into a new
space. There is no natural way to compare such embeddings to one another because
the shape of the geometric space itself depends on the entire graph. For example,
the placement of the origin and axes in one embedding need not have any particular
relationship to the origin and axes in others.
This creates a problem when the goal is to understand what has changed in the
structure of the graph from one time to another. It is, of course, possible to make
qualitative statements (“these two nodes seem to have become less related”) but it is
hard to make such statements rigorous. It is also impossible to define the trajectory
of a single node over time since there is no common space within which such a
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Modelling relationships
that change over time
So far, all of our social networks have assumed that relationships are static: they
either exist or not between any pairs of nodes, and intensities, as described by edge
weights, do not change. This is not very realistic. Relationships are created (and
sometimes lapse), and the intensity of any particular relationship ebbs and flows
over time. It is useful to be able to model the effect of each of these changes on
the overall structure of the social network, and so we turn our attention to modelling
edges whose intensities change with time. We include in this edges that may come
into existence (that is, a change from an intensity of zero to a non-zero value), and
that disappear (that is, a change from a non-zero intensity to an intensity of zero).
7.1 Temporal networks
Temporal (dynamic) social network analysis aims to understand the structures in networks as they evolve, building on static analysis techniques but adding a mechanism
for variation with time.
The benefits, and drawbacks, of graph representations of relationships is that
a single change, for example the addition or deletion of an edge, can change the
entire graph structure. When a social network changes from one time to another,
reflecting this change completely requires a fresh embedding of the graph into a new
space. There is no natural way to compare such embeddings to one another because
the shape of the geometric space itself depends on the entire graph. For example,
the placement of the origin and axes in one embedding need not have any particular
relationship to the origin and axes in others.
This creates a problem when the goal is to understand what has changed in the
structure of the graph from one time to another. It is, of course, possible to make
qualitative statements (“these two nodes seem to have become less related”) but it is
hard to make such statements rigorous. It is also impossible to define the trajectory
of a single node over time since there is no common space within which such a
81