Visual Complexity: Mapping Patterns of Information

Referring to the book Visual Complexity: Mapping Patterns of Information

Networks are graphs

and we agree that a tree is a special type of graph with the topology that we know.

Fig 2 The tree of streets - Ch 2 P 47

Hierarchical by connectivity. Striking visual display by mapping the measure of connectivity to the width of the branch of the given street. Unclear how and if topology is preserved.

Fig 3 Sets vs tree / semilattice - Ch 2 P 47

A non-overlapping powerset (where each node is only contained in nested sets) transforms to a tree.

An overlapping powerset produces a semilattice (is this the graph theory name?) in which all nodes can be connected to multiple parents.

Set containment can be mapped to a graph through this algorithm:

set_to_graph( powerset ) :
/* powerset is list of sets. each set is list of its subsets. */

for each set in powerset ordered by cardinality descending parents = [] create node indexed by set for each set of higher cardinality ordered by cardinality ascending as candidate parent if set contained in candidate parent and candidate parent does not contain any of parents[] parents[] = candidate parent link node to parent node by looking up node of candidate parent

Is It possible to design reversible algorithms ?

i.e. given the output produce the input

Simplest way: store the input and index it with output.

What if same output is produced by several inputs? Should return input "template" - what patterns of input produce this output.
Or can return all inputs that historically have produced this output.

But what I mean is a function that can run in reverse algorithmically, not through memory.
e.g. can the function set_to_tree be written such that tree_to_set be automatically derived?

Fig 10 Network models - Ch 2 P 55

Clarifying diagram of the difference between:

  • centralized graph: one center to which all nodes are connected (tree with single-level branches)
  • decentralized graph: several interconnected centers to which remaining nodes are connected (is this a tree?)
  • distributed graph: nodes are arranged in a lattice where each node is connected to a certain maximum number of neighbours (is this a lattice?)

There is a progression centralized -> decentralized -> fractal decentralization that does not reach distribution. Instead, a new event must be introduced which is the severance of a connection between a node and its parent.

Also, how to obtain the semilattice from the centralized graph?

Fig 13 Zones of influence - Ch 2 P 58

The visualisation depicts the proximity of nodes in the European political blogosphere. Sites are organized by the amount of "interactions" between them (links I assume).

One can imagine visualising the ebbs and flows of influence of large clusters over time. This can reveal political influences as they grow stronger or weaker. Simply perform an animation of the visualisation at different timestamps, provided the data is correlated across snapshots.

It would be interesting to add to this graph the readership of each site - anonymously of course :-) - to visualise the actual citizen political influence.