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- 1. Dynamics in Graph Analysis Adding Time as Structure for Visual and Statistical Insight Benjamin Bengfort @bbengfort District Data Labs
- 2. Are graphs effective for analytics? Or why use graphs at all?
- 3. Algorithm Performance More understandable implementations and native parallelism provide benefits particularly to machine learning. Visual Analytics Humans can understand and interpret interconnection structures, leading to immediate insights.
- 4. “Graph technologies ease the modeling of your domain and improve the simplicity and speed of your queries.” — Marko A. Rodriguez http://bit.ly/2cthd2L
- 5. Construction Given a set of [paths, vertices] is a [constraint] graph construction possible? Existence Does there exist a [path, vertex, set] within [constraints]? Optimization Given several [paths, subgraphs, vertices, sets] is one the best? Enumeration How many [vertices, edges] exist with [constraints], is it possible to list them?
- 6. Traversals
- 7. Property Graphs
- 8. How do you model time?
- 9. Relational Database
- 10. Time Properties
- 11. Time Modifies Traversal
- 12. Example of Time Filtered Traversal: Data Model Name: Emails Sent Network Number of nodes: 6,174 Number of edges: 343,702 Average degree: 111.339
- 13. def sent_range(g, before=None, after=None): # Create filtering function based on date range. def inner(edge): if before: return g.ep.sent[edge] < before if after: return g.ep.sent[edge] > after return inner def degree_filter(degree=0): # Create filtering function based on min degree. def inner(vertex): return vertex.out_degree() > degree return inner Example of Time Filtered Traversal
- 14. print("{} vertices and {} edges".format( g.num_vertices(), g.num_edges() )) # 6174 vertices and 343702 edges aug = sent_range(g, after=dateparse("Aug 1, 2016 09:00:00 EST") ) view = gt.GraphView(g, efilt=aug) view = gt.GraphView(view, vfilt=degree_filter()) print("{} vertices and {} edges".format( view.num_vertices(), view.num_edges() )) # 853 vertices and 24813 edges Example of Time Filtered Traversal
- 15. What makes a graph dynamic?
- 16. Time Structures Perform static analysis on dynamic components with time as a structure. Dynamic Graphs Multiple subgraphs representing the graph state at a discrete timestep.
- 17. Keyphrases over Time
- 18. Natural Language Graph Analysis: Data Ingestion
- 19. Natural Language Graph Analysis: Data Modeling Name: Baleen Keyphrase Graph Number of nodes: 2,682,624 Number of edges: 46,958,599 Average degree: 35.0095 Name: Sampled Keyphrase Graph Number of nodes: 139,227 Number of edges: 257,316 Average degree: 3.6964
- 20. def degree_filter(degree=0): def inner(vertex): return vertex.out_degree() > degree return inner g = gt.GraphView(g, vfilt=degree_filter(3)) Name: High Degree Phrase Graph Number of nodes: 8,520 Number of edges: 112,320 Average degree: 26.366 Natural Language Graph Analysis: Data Wrangling
- 21. Basic Keyphrase Graph Information Vertex Type Analysis Primarily keyphrases and documents. Degree Distribution Power laws distribution of degree.
- 22. Natural Language Graph Analysis: Data Wrangling def ego_filter(g, ego, hops=2): def inner(v): dist = gt.shortest_distance(g, ego, v) return dist <= hops return inner # Get a random document v = random.choice([ v for v in g.vertices() if g.vp.type[v] == 'document' ]) ego = gt.GraphView( g, vfilt=ego_filter(g,v, 1) )
- 23. The Centrality of Time
- 24. Extract Week of the Year as Time Structure # Construct Time Structures to Keyphrase h = gt.Graph(directed=False) h.gp.name = h.new_graph_property('string') h.gp.name = "Phrases by Week" # Add vertex properties h.vp.label = h.new_vertex_property('string') h.vp.vtype = h.new_vertex_property('string') # Create graph from the keyphrase graph for vertex in g.vertices(): if g.vp.type[vertex] == 'document': dt = g.vp.pubdate[vertex] weekno = dt.isocalendar()[1] week = h.add_vertex() h.vp.label[week] = "Week %d" % weekno h.vp.vtype[week] = 'week' for neighbor in vertex.out_neighbours(): if g.vp.type[neighbor] == 'phrase': phrase = h.add_vertex() h.vp.vtype[vidmap[phrase]] = 'phrase' h.add_edge(week, phrase)
- 25. PageRank Centrality A variant of Eigenvector centrality that has a scaling factor and prioritizes incoming links. Eigenvector Centrality A measure of relative influence where closeness to important nodes matters as much as other metrics. Degree Centrality A vertex is more important the more connections it has. E.g. “celebrity”. Betweenness Centrality How many shortest paths pass through the given vertex. E.g. how often is information flow through?
- 26. What are the central weeks and phrases? Betweenness Centrality Katz Centrality
- 27. Keyphrase Dynamics
- 28. Create Sequences of Time Ordered Subgraphs
- 29. Animating Dynamics
- 30. Network Visualization
- 31. Layout: Edge and Vertex Positioning Fruchterman Reingold SFDP (Yifan-Hu) Force Directed Radial Tree Layout by MST ARF Spring Block
- 32. Visual Properties of Vertices Lane Harrison, The Links that Bind Us: Network Visualizations http://blog.visual.ly/network-visualizations
- 33. Visual Properties of Edges Lane Harrison, The Links that Bind Us: Network Visualizations http://blog.visual.ly/network-visualizations
- 34. Visual Analysis
- 35. The Visual Analytics Mantra Overview First Zoom and Filter Details on Demand
- 36. Questions?

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