Notebook

In [2]:

%run "libraries.ipynb"

from IPython.display import display, HTML
from IPython.html import widgets
import matplotlib.patheffects as path_effects

:0: FutureWarning: IPython widgets are experimental and may change in the future.

In [3]:

hyperlinks_graph = nx.read_gexf("data/hyperlinks.gexf")

In [4]:

g = nx.DiGraph()

nb_out = 3

hyperlinks_graph.remove_nodes_from([ "Geometry", "Mathematics" ])

for u in hyperlinks_graph:
    nb = sorted(hyperlinks_graph[u].items(), key=lambda x: -x[1]["term occurence"])
    
    # filtering self loops
    nb = [ n for n in nb if n[0] != u ]

    for v in nb[0:nb_out]:
        #print v
        g.add_edge(u, v[0], attr_dict=v[1])

In [5]:

print "reduced graph"
print "============="
print "nodes: %s" % (len(g.nodes()))
print "edges: %s" % (len(g.edges()))
print "reduction: %s/%s (%s)" % (len(g.edges()),
                                 len(hyperlinks_graph.edges()),
                                 float(len(g.edges()))/float(len(hyperlinks_graph.edges())))

reduced graph
=============
nodes: 296
edges: 838
reduction: 838/3469 (0.241568175267)

In [6]:

nx.write_gexf(g, "data/reading_maps/pages-hyperlinks-reduced-3.gexf")

community detection¶

In [7]:

import community
partitions = community.best_partition(g.to_undirected())

In [8]:

def print_groups(communities):
    html = "<table>"

    for c, ps in communities.iteritems():
        html += "<tr><td style=\"width: 100px; text-align: center; \"><h3>group %s</h3></td><td>" % (c)
        html += ", ".join(map(lambda x: u"<a href=\"http://en.wikipedia.org/wiki/{0}\" target=\"_blank\">{0}</a>".format(x), ps))
        html += "</td></tr>"
    
    html += "</table>"

    display(HTML(html))
        
communities = {}
for k, v in partitions.iteritems():
    communities.setdefault(v, []).append(k)


print_groups(communities)

group 0	Discrete geometry, Pi, Point in polygon, Convex hull, Star polygon, Wallpaper group, Polygon triangulation, Penrose tiling, Polygon, Euclidean shortest path, Prototile, Aperiodic tiling, Honeycomb (geometry), Crystal, Internal and external angle, Zonohedron, Regular Polytopes (book), Fractal, Polyhedron, Delaunay triangulation, Quasicrystal, Voronoi diagram, Wallace–Bolyai–Gerwien theorem, Uniform tessellation, Pattern, Wang tile, Dissection problem, Computational geometry, Tessellation, Hilbert's third problem, Schläfli symbol, Archimedean solid, Graham scan, Rhombus
group 1	Invariant (mathematics), Annulus (mathematics), Pappus's centroid theorem, Parametric surface, Birational geometry, Systolic geometry, Mathematics and fiber arts, Torus, Heronian triangle, Pythagorean triple, Heronian tetrahedron, Spline (mathematics)
group 2	Triangle inequality, Spherical trigonometry, Symmedian, Point (geometry), Squaring the circle, Isosceles trapezoid, Napkin ring problem, Equilateral triangle, List of circle topics, Distance geometry, Acute and obtuse triangles, Incircle and excircles of a triangle, Holditch's theorem, Cavalieri's principle, Tangential quadrilateral, Rectangle, Heron's formula, Circumscribed circle, Brahmagupta's formula, List of triangle inequalities, Ptolemy's theorem, Van Hiele model, Nine-point circle, Angle trisection, Inscribed angle, Dividing a circle into areas, Trigonometry, Quadrilateral, Kite (geometry), Orthodiagonal quadrilateral, Pons asinorum, Central angle, Altitude (triangle), Euclidean geometry, Equidiagonal quadrilateral, Trapezoid, Sphericon, Euclidean distance, Orthocentric system, Euler line, Right triangle, Isosceles triangle, Homothetic center, Integer triangle, Synthetic geometry, Pythagorean theorem, Reuleaux triangle, Bretschneider's formula, Pedal triangle, List of triangle topics, Parallelogram law, Thales' theorem, List of trigonometry topics, Angle, Triangle, Concyclic points, Bicentric quadrilateral, Cyclic quadrilateral, The Method of Mechanical Theorems, Parallel postulate, Point group
group 3	Shear mapping, Prismatoid, Kepler–Poinsot polyhedron, Kissing number problem, Regular polytope, Ehrhart polynomial, Polytope compound, Convex uniform honeycomb, Polytope, Deltahedron, N-sphere, Prism (geometry), Platonic solid, Dihedral angle, Normal (geometry), Angular defect, Uniform polyhedron, Four-dimensional space, Johnson solid, Pick's theorem, Tetrahedron, Hyperplane
group 4	Circle, Poncelet–Steiner theorem, Contact geometry, Golden angle, Square, Power center (geometry), Analytic geometry, Coordinate-free, Curve of constant width, Isoperimetric inequality, Pyramid (geometry), Shape, Straightedge, Mrs. Miniver's problem, Compass-and-straightedge construction, Geometric shape, Symplectic geometry
group 5	Dandelin spheres, Parametric equation, Semi-major axis, Soddy's hexlet, Similarity (geometry), Pascal's theorem, Hyperplane at infinity, Matrix representation of conic sections, Plane at infinity, Strähle construction, Hyperbola, Concurrent lines, Astronomy, Sangaku, Pappus's hexagon theorem, Parabola, Line at infinity, Pedoe's inequality, Locus (mathematics), Ellipse
group 6	Steiner chain, Klein geometry, Descriptive geometry, Riemann sphere, Inversive geometry, Minkowski space, Parabolic geometry (differential geometry), Projective geometry, Riemannian geometry, Information geometry, List of interactive geometry software, Cross-ratio, Projective line over a ring, Homothetic transformation, Projective line, Conformal geometry, Pseudosphere, Ruppeiner geometry, Affine transformation, Affine space, Affine geometry, Lie sphere geometry, 3D projection, Hyperbolic geometry, Arc (projective geometry), Möbius transformation, Differential geometry, Stereographic projection, Homography, Projective space
group 7	Elliptic geometry, Complex geometry, Geometrization conjecture, Enumerative geometry, Eccentricity (mathematics), Paraboloid, Cone, Focus (geometry), Parabolic reflector, Algebraic geometry, Group action, Kepler conjecture, Topology, Complex projective plane, Quadric, Borromean rings, Conic section, Finite geometry, Sphere, Spheroid, Oval (projective plane), Point at infinity, 3-sphere, Quantum geometry, Solid geometry, Parabolic microphone, Toric variety, Ellipsoid, Tropical geometry, Sphere packing, Projective plane, Spherical geometry, Noncommutative geometry, Hyperboloid
group 8	Bézier curve, 2D geometric model, 3D computer graphics, Duality (projective geometry), 2D computer graphics, Mathematical morphology, Digital geometry, Ray tracing (graphics), Non-uniform rational B-spline, Image analysis, Homogeneous coordinates, B-spline, Hidden line removal, Cross section (geometry), Binary space partitioning, Computer graphics, Minkowski addition, Constructive solid geometry, Point location
group 9	Absolute geometry, Ordered geometry, Girard Desargues, Incidence (geometry), Non-Euclidean geometry, Line (geometry), Desargues' theorem, Monge's theorem, Incidence geometry, Taxicab geometry, Ball (mathematics), Hilbert's axioms
group 10	Crystal system, Integral geometry, Polar sine, Geometry of numbers, Minkowski's theorem, Parallelepiped, Lattice (group), Rotation (mathematics), Symmetry group, Hadwiger's theorem, Convex geometry
group 11	Congruence (geometry), Point groups in three dimensions, Root system, Reflection (mathematics), Erlangen program, Leech lattice, Parallel (geometry), Space group, Relative direction, Infinitesimal transformation, Frieze group, Coordinate rotations and reflections, Isometry, Symmetry, Glide reflection, Roman surface, Coxeter group, Translation (geometry), Point groups in two dimensions, Translational symmetry, Mirror image, Handedness, Chirality (mathematics), Transformation geometry

subgraphs explorer¶

In [9]:

%config InlineBackend.figure_formats=['svg']

def map_colors(g ,partitions):
    size = np.max( [ x[1] for x in partitions.iteritems() ])
    
    for n in partitions:
        g.node[n]["color"] = float(partitions[n])/float(size)


map_colors(g, partitions)

pages = g.nodes()
pages = sorted(pages)

color_map = plt.get_cmap("Set2")
# color_map = sns.color_palette("Set2", 11)

print color_map
def display_local_graph(page):
    nbunch = [ page ]
    nbunch.extend( list(g.to_undirected()[page]))
    g_sub = g.subgraph(nbunch)

    #nx.draw_spring(g2)
    pos = nx.spring_layout(g_sub,iterations=150)
   
    plt.figure(figsize=(6,6))

    colors = map(lambda x: g.node[x]["color"], g_sub.nodes())
    
    # draw nodes
    nodes = nx.draw_networkx_nodes(g_sub, pos, alpha=0.9, node_size=500, node_color=colors, cmap=color_map, vmin=0, vmax=1)
    nodes.set_edgecolor('w')

    # draw edges
    nx.draw_networkx_edges(g_sub, pos, alpha=0.3, width=1)
    
    # draw labels
    labels = nx.draw_networkx_labels(g_sub, pos, font_size=8, font_family="Bitstream Vera Sans")
    map(lambda x: labels[x].set_path_effects([path_effects.Stroke(linewidth=1, foreground='white'),
                       path_effects.Normal()]),labels)
    
    plt.axis('off')
    plt.show()


w = widgets.Select(description="page", options=pages)
widgets.interact(display_local_graph, page=w);

community detection¶

group 0

group 1

group 2

group 3

group 4

group 5

group 6

group 7

group 8

group 9

group 10

group 11

subgraphs explorer¶