xii
Preface
the intensity of B’s relationship to A; indeed, A may have a relationship to B, while
B has no relationship to A. Not all relationships are positive. A may be a friend or
ally of B but an enemy of C. We need a way to model relationships of both kinds.
Finally, the existence and intensity of relationships change with time, and a way to
represent the changing structure of each social network is needed.
There has been research work investigating how to add these properties to social network analysis. The contribution of this book is to show that there is a single
idea, which can be worked out in constructions, that solves all of these problems
in essentially the same way. All of the properties described above are properties of
the edges: edge types can be modelled as a property such as color, intensities as associated weights, asymmetries by directing the edges, and positivity and negativity
by allowing weights to be both positive and negative. The key idea is that, instead
of trying to model all of these possibilities at once, the nodes of the network are
replicated into versions, each of which is associated with a property, and the original
edges are connected to these versions in ways that capture and preserve their original
semantics. The resulting graph is (notionally) much larger, but its edges are ordinary,
and standard techniques can be used to analyze them. Of course, the analysis must
take account of the multiple versions of the nodes, but this turns out be a win because
the relationships among the versions themselves reveal aspects of the structure.
We show how this works out both mathematically, and with sets of examples
that illustrate, sometimes forcefully, that the social network that represents these
richer properties is very different from a representation in which they are ignored or
conflated.
Preface
the intensity of B’s relationship to A; indeed, A may have a relationship to B, while
B has no relationship to A. Not all relationships are positive. A may be a friend or
ally of B but an enemy of C. We need a way to model relationships of both kinds.
Finally, the existence and intensity of relationships change with time, and a way to
represent the changing structure of each social network is needed.
There has been research work investigating how to add these properties to social network analysis. The contribution of this book is to show that there is a single
idea, which can be worked out in constructions, that solves all of these problems
in essentially the same way. All of the properties described above are properties of
the edges: edge types can be modelled as a property such as color, intensities as associated weights, asymmetries by directing the edges, and positivity and negativity
by allowing weights to be both positive and negative. The key idea is that, instead
of trying to model all of these possibilities at once, the nodes of the network are
replicated into versions, each of which is associated with a property, and the original
edges are connected to these versions in ways that capture and preserve their original
semantics. The resulting graph is (notionally) much larger, but its edges are ordinary,
and standard techniques can be used to analyze them. Of course, the analysis must
take account of the multiple versions of the nodes, but this turns out be a win because
the relationships among the versions themselves reveal aspects of the structure.
We show how this works out both mathematically, and with sets of examples
that illustrate, sometimes forcefully, that the social network that represents these
richer properties is very different from a representation in which they are ignored or
conflated.