To Do
- If we have an event driven time version of our graph, and we want to specify a , what is the method/mapping for doing that flattening?
- This is the mapping of event driven time to an evenly spaced time (wall clock time)
- Or, from one to another which could be larger
- What happens to the node identities with regard to this flatting down of time?
- What about if a node merges with another or splits?
- What if an edge comes and goes inside of one ? Do we consider that a connection there, or not? Is it shown or not? How does that translate under mapping to a different value?
- DONE Look back at Bruno’s paper to see what they considered if an edge both came and went inside of one timestep. Did they consider it? If it doesn’t say, email and ask him about it.
- They just do the union of all edges during the interval.
- When mapping, what do we do?
- aggregate the changes that happen inside one time unit? If there are two things (edge create, edge delete), what happens if they undo each other in the same timestep?
- aggregate the changes into the next timestep? (everything that happens changes the graph, and it’s apparent at the next time step)
- morph time so that an even number of things happen in each timestep, although we’ve now messed up ’s spacing?
- (low prio) Merging and splitting of nodes in a graph
- Even under one identity mapping, what happens when nodes split? Think circuses or corporate identities
- If “flattening” the graph for the future (think ), what do you do if a node has split (or merged)? Do you consider them to be separate nodes? Are the edges still connected to the one node or multiple nodes? One thought would be a super node with the smaller nodes inside of it (so some connection to each other, but not an edge-like connection–an identity connection).
- We need to know this when comping a measure for the “rest of time.”
- (low prio) Write paragraphs on the distance measures (and how they might take into account ordering of edges)
- Physical constraints on what counds as a path (ie ordering in time)
- This would be things like traffic patterns, information that spreads through sets of phone calls, etc
- Kinds of things that can be encoded in the distance metric itself. There’s an inherent caveat on the distance metric in a directed graph vs an undirected graph, namely that an edge can only be traversed (distance calculated) if it’s travelling in the right direction.
- We want to characterize the dynamics of the graph, which these current metric extensions I’ve done is missing
- This is the value of the metrics we’re creating
- What about doing the metrics over time intervals? (so instead of t, have (t1, t2)). What about all the other segments of time from the earlier Evolving Networks definition?
- Possible changes in edges (without changing the identity) could be a reversal of direction
- Parameterize the definitions better. For example, , where and we’re considering a specific identity . The entire graph should be a parameter, not just the identity.
- Specify exactly the definition of “flattening” for .
- DONE Fix ’s definition to use .
- Better define as it relates to . Worthy would rather see everything parameterized than using subscripts and superscripts.
- DONE Review Tang’s paper again to know exactly what their path definition is (are they inserting transitive links within each snapshot, or is the path actually listing every node at every time?), the exact definition of , and centrality as it relates to time . ( has received or is holding a message at time ?)