Link Communities Reveal
Multiscale Complexity in Networks



                     Yong-Yeol Ahn
   Center for Complex Netw...
Sune Lehmann



James P. Bagrow
Communities
Communities
“a group of densely
interconnected nodes”
in understanding and visualizing the structure of net-
                      works. In this paper we show how this can be ...
arXiv:cond-m                                                                     a
                                       ...
Why bother?
Hierarchical organization


  Community overlap
Hierarchical organization
partitioning in graph theory and computer science, and




FIG. 1: A small network with community structure of the
Hierarchical community
       structure


Hierarchy    Communities
Hierarchical Random Graph model




               Clauset et al., Nature (2008)
neously explain and                                 to observed network data using the tools of statistical inf
only obser...
But,
Community overlap
ciated     large network we introduce the distributions of these four basic
 priori    quantities. In particular we focus ...
A                         B




                          Multiple Contexts

C overlap and hierarchy        Family
    do ...
A                         Multiple Contexts
                          B

                            Multiple Contexts

  ...
C overlap and hierarchy                   Family
    do not mix                                     buildings in same
    ...
Hierarchical community
       structure


Hierarchy    Communities
Hierarchy        Communities




  Complex global structure
Colleagues

Family

Friends
Overlap is
pervasive
Overlap is
pervasive
Simple local structure
Complex global structure
Complex global structure
Example:
What is this?
What the xxxx
  is this?
measures, and second, these measures are, crucially, recalculated after each removal. We also propose
             a measu...
above, because none of the others in the literature satisfy all these     of protein–protein interactions27 (Fig. 2c). The...
a Link communities and Bob also work together b
             Spouses Alice                                                ...
pping community structure around Acetyl-CoA in the E. coli metabolic network. Acetyl-CoA plays several
tant roles in metab...
Then, how can we find
hierarchical community
       structure
in COMPLEX networks
with pervasive overlap?
Our solution:
 Use Links
Our solution:
 Use Links
Our solution:
    Use Links

  “a group of densely
interconnected nodes”
Our solution:
    Use Links

  “a group ofTopologically
            densely
     Similar
interconnected nodes”
           ...
Colleagues

Family

Friends
Colleagues

         ‘Family’ links
Family
            Friends
Colleagues

                       ‘Family’ links
Friends
              Family




‘Friends’ links
‘Nerds & geeks’ links
       Colleagues


                       ‘Family’ links
Friends
              Family




‘Friends’...
Nodes: multiple membership

 Links: unique membership
Overlap
Overlap
Hierarchy   Communities
Hierarchy   Communities
Reconciliation
So, How?
Similarity between links




Hierarchical Clustering
Hierarchical Link
Clustering (HLC)
A                                                 B
             ei k                     ejk                      c

    ...
A                                                 B
             ei k                     ejk                          c

...
(a)   1
              2               (c)
      3                                                                         ...
?
Partition Density

Community c has mc edges and nc induced nodes
          c     mc           nc
Partition Density
Community c has mc edges and nc induced nodes
          c     mc           nc
Partition Density
Community c has mc edges and nc induced nodes
          c     mc           nc




       mc = 8         ...
Partition Density
Community c has mc edges and nc induced nodes
          c     mc           nc



                     = ...
Partition Density
Community c has mc edges and nc induced nodes
          c     mc           nc



            −        = ...
Partition Density
Community c has mc edges and nc induced nodes
          c     mc           nc


        −
              ...
Partition Density

 −
           mc − (nc − 1)
      =   nc (nc −1)
 −             2 − (nc − 1)
          mc − (nc − 1)
  ...
Partition Density
  −
                mc − (nc − 1)
           =   nc (nc −1)
  −                 2 − (nc − 1)
           ...
It’s just density


No resolution limit
Boulatruelle
                             Jondrette
                                                     Brujon
          ...
Does it really work?
Quantitative Evaluation Framework
Quantitative Evaluation Framework


                      How homogeneous each
Community quality        community is?

   ...
Quantitative Evaluation Framework


                      How homogeneous each
Community quality        community is?

   ...
Quantitative Evaluation Framework


                      How homogeneous each
Community quality        community is?

   ...
Quantitative Evaluation Framework


                      How homogeneous each
Community quality        community is?

   ...
Metadata




Figure R11: Example of the network and available metadata for the Amazon.com product co-purchases network. He...
Quantitative Evaluation Framework

Community quality            Amazon.com                    Community coverage          ...
and topologies (for example, the network range from sparse (average degree 6.34) to dense (average degree 38.95)).
       ...
! ('                                                                                                                      ...
,$-+.%$+
                                                                   2S89C;4(12S89;F8
                             ...
d as soc.
              Wor
                                                                 ,$-+.%$+
                    ...
Examples
BROOM
                               PAINT
        SWEEP
                                          PAINTER


GROOM
       ...
!   '89:;<=>>?98@8AB;CD=?9E;!"#$%!;FD=>;@GA;(=DE;&BB=<8C@8=9;9A@H=D:

                "&'()*+(,-./01*(,1(
                ...
/   34(5&,-.."(46417&'8-"()&&'"$9!"#$&:8-.&;;<&='00>

                      %&'()*+,


                                   ...
B




      proteasome core complex (GO:005839, C)
      threonine-type endopeptidase activity (GO:0004298, F)
           ...
B                       103
    number of communities

                                                                   ...
u rren cies
B                           3                                                       C
    number of communitie...
Hierarchical
organization
~600k nodes
~3M edges
threshold = 0.20
threshold = 0.20
threshold = 0.20
threshold = 0.20
threshold = 0.20
A               B                   threshold = 0.23


        50 km

                        thr =
                      ...
Remaining
                                                                          hierarchy

 e        1
               ...
a                    b              Planets
                                                                              ...
Conclusion
• Link viewpoint effectively removes
  the problem of overlap.
• Global hierarchical structure can be
  found by...
Acknowledgements
Acknowledgements
A.-L. Barabási, H. Yu, S. Ahnert, J. Park, D.-
S. Lee, P.-J. Kim, M. A. Yildirim,
Acknowledgements
A.-L. Barabási, H. Yu, S. Ahnert, J. Park, D.-
S. Lee, P.-J. Kim, M. A. Yildirim,


       T. S. Evans, R...
xkcd.com
a         Spouses Alice and Bob also work together   b                      Word Association examples
    Link communities...
link communities
 a     Internal groups without distinguishing features are undetectable to ALL methods
                  ...
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Link communities reveal multiscale complexity in networks
Upcoming SlideShare
Loading in...5
×

Link communities reveal multiscale complexity in networks

6,292

Published on

Link communities reveal multiscale complexity in networks

Yong-Yeol Ahn, James P. Bagrow & Sune Lehmann

Nature (2010) doi:10.1038/nature09182

Published in: Technology
0 Comments
8 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
6,292
On Slideshare
0
From Embeds
0
Number of Embeds
4
Actions
Shares
0
Downloads
184
Comments
0
Likes
8
Embeds 0
No embeds

No notes for slide
















  • organizing principle, underlying mechanism, dynamics, function

  • provide context, provide detail.
  • provide context, provide detail.















































































































































  • Link communities reveal multiscale complexity in networks

    1. 1. Link Communities Reveal Multiscale Complexity in Networks Yong-Yeol Ahn Center for Complex Network Research, Northeastern University
    2. 2. Sune Lehmann James P. Bagrow
    3. 3. Communities
    4. 4. Communities
    5. 5. “a group of densely interconnected nodes”
    6. 6. in understanding and visualizing the structure of net- works. In this paper we show how this can be achieved. pr arXiv:cond-mat/0308 “a group of densely The study of community structure in networks has a long history. It is closely related to the ideas of graph nic era partitioning in graph theory and computer science, and th interconnected nodes” ing a op th rit ev sta if nit mu wh th mi be
    7. 7. arXiv:cond-m a op th rit ev sta if nit mu wh th mi be Hundreds of community FIG. 1: A small network with community structure of the type considered in this paper. In this case there are three us communities, denoted by the dashed circles, which have dense wi detection methods internal links but between which there are only a lower density of external links. ing div
    8. 8. Why bother?
    9. 9. Hierarchical organization Community overlap
    10. 10. Hierarchical organization
    11. 11. partitioning in graph theory and computer science, and FIG. 1: A small network with community structure of the
    12. 12. Hierarchical community structure Hierarchy Communities
    13. 13. Hierarchical Random Graph model Clauset et al., Nature (2008)
    14. 14. neously explain and to observed network data using the tools of statistical inf only observed topo- ence, combining a maximum likelihood approach [15] w as right-skewed de- a Monte Carlo sampling algorithm [16] on the space of fficients, and short knowledge of hier- ict missing connec- high accuracy, and han competing tech- suggest that hierar- complex networks, network phenom- devoted to the study n networks [5, 6, 9, nd simple clustering, G. 1: A hierarchical network with structure on many scales and ation at hierarchical random graph. Each internal node r corresponding all scales in he dendrogram is associated with a probability p that a pair of r tices hierarchical struc- y, in the left and right subtrees of that node are connected. (The des of the internal nodes in the figure represent the probabilities.) am in which closely mmon ancestors that ore distantly related ability of a connec- Clauset et al., Nature (2008)
    15. 15. But,
    16. 16. Community overlap
    17. 17. ciated large network we introduce the distributions of these four basic priori quantities. In particular we focus on their cumulative distribution ins5,6, o the es of e net- actual ps of main mmu- ucture eristic ficient scale. ns we ies of raphs ns and nodes est of usters, ve no G. Palla, I. Derényi, I. Farkas & T. Vicsek, Nature, 2005
    18. 18. A B Multiple Contexts C overlap and hierarchy Family do not mix buildings in same neighborhood University home and work
    19. 19. A Multiple Contexts B Multiple Contexts Multiple Contexts C overlap and hierarchy Family do not mix Multiple Contexts buildings in same neighborhood University home and work
    20. 20. C overlap and hierarchy Family do not mix buildings in same neighborhood University home and work joint appointment D 1 2 F Single dendrogram cannot represent multiple hierarchical contexts 3 3! 4
    21. 21. Hierarchical community structure Hierarchy Communities
    22. 22. Hierarchy Communities Complex global structure
    23. 23. Colleagues Family Friends
    24. 24. Overlap is pervasive
    25. 25. Overlap is pervasive
    26. 26. Simple local structure
    27. 27. Complex global structure
    28. 28. Complex global structure
    29. 29. Example:
    30. 30. What is this?
    31. 31. What the xxxx is this?
    32. 32. measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on What the xxxx the sometimes dauntingly complex structure of networked systems. I. INTRODUCTION hierarchical clustering in sociology [18, 19]. Before pre- senting our own findings, it is worth reviewing some of this preceding work, to understand its achievements and is this? Empirical studies and theoretical modeling of networks have been the subject of a large body of recent research in where it falls short. statistical physics and applied mathematics [1, 2, 3, 4]. Graph partitioning is a problem that arises in, for ex- Network ideas have been applied with great success to ample, parallel computing. Suppose we have a num- topics as diverse as the Internet and the world wide ber n of intercommunicating computer processes, which web [5, 6, 7], epidemiology [8, 9, 10, 11], scientific ci- we wish to distribute over a number g of computer proces- tation and collaboration [12, 13], metabolism [14, 15], sors. Processes do not necessarily need to communicate and ecosystems [16, 17], to name but a few. A property with all others, and the pattern of required communica- that seems to be common to many networks is commu- tions can be represented by a graph or network in which nity structure, the division of network nodes into groups the vertices represent processes and edges join process within which the network connections are dense, but be- pairs that need to communicate. The problem is to allo- tween which they are sparser—see Fig. 1. The ability to cate the processes to processors in such a way as roughly find and analyze such groups can provide invaluable help to balance the load on each processor, while at the same in understanding and visualizing the structure of net- time minimizing the number of edges that run between works. In this paper we show how this can be achieved. processors, so that the amount of interprocessor commu- The study of community structure in networks has a nication (which is normally slow) is minimized. In gen- long history. It is closely related to the ideas of graph eral, finding an exact solution to a partitioning task of partitioning in graph theory and computer science, and this kind is believed to be an NP-complete problem, mak- ing it prohibitively difficult to solve for large graphs, but a wide variety of heuristic algorithms have been devel- oped that give acceptably good solutions in many cases, the best known being perhaps the Kernighan–Lin algo- rithm [20], which runs in time O(n3 ) on sparse graphs. A solution to the graph partitioning problem is how- ever not particularly helpful for analyzing and under- standing networks in general. If we merely want to find if and how a given network breaks down into commu- nities, we probably don’t know how many such com- munities there are going to be, and there is no reason why they should be roughly the same size. Furthermore, the number of inter-community edges needn’t be strictly minimized either, since more such edges are admissible between large communities than between small ones. FIG. 1: A small network with community structure of the As far as our goals in this paper are concerned, a more useful approach is that taken by social network analysis
    33. 33. above, because none of the others in the literature satisfy all these of protein–protein interactions27 (Fig. 2c). These pictures ca requirements simultaneously21,24. tests or validations of the efficiency of our algorithm. In p Word association network: Network of “commonly associated English words” Figure 2 | The community structure around a particular node in three be associated with his fields of interest. b, The communities of t different networks. The communities are colourG. Palla, I. Derényi, I. Farkas & T. Vicsek, Nature, 2005 w* coded, the overlapping ‘bright’ in the South Florida Free Association norms list (for
    34. 34. a Link communities and Bob also work together b Spouses Alice Word Association examples Link communities COMBINE COMBINE JOIN Alice FRUIT BLENDER JOIN Alice FRUIT INTEGRATE BLENDER INTEGRATE Bob JUICE BLEND Bob JUICE BLEND MIX MIXTURE Family Work MIX MIXTURE Family Work Node communities Node communities Figure S16: Overlapping community structure around Acetyl-CoA in the E. coli metabolic network. Alice Alice different and important roles in metabolism. Shown are only communities with homogeneity score e DISAPPEAR inside each community share at least one pathway annotation); all other links, including those that Alice Alice LOOK structure, are omitted. Pathway annotations shared by all community members are displayed with c LOOK APPEAR DISAPPEAR two communities to the right of Acetyl-CoA are grouped since they share the same exact pathway an APPEAR VANISH Bob Bob SEE VANISH Bob Bob Work SEE REAPPEAR Family REAPPEAR Work SHOW ATTEND Family The Alice-Bob link was placed in family but both SHOW ATTEND The Alice-Bobwork was placed in are identified home and link relationships family but both home and work relationships are identified BROOM PAINT Figure S4: Overlapping links. In the link community framework, a link may beSWEEP assigned to only one community. By de gure S4: Overlapping links. In the link community framework, a link may be relationships betweencommunity. By derivi node communities, however, the problem of effectively discovering multiple assigned to only one nodes is effectively s PAINTER ode communities, however,many communities together regardless of the membership of the link betweenis effectively illust Two nodes can belong to the problem of effectively discovering multiple relationships between nodes them. Left: solv GROOM wo nodes can belong to manyexamples from word association network. In the upper example, Blend and blender belong to of the situation. Right: real communities together regardless of the membership of the link between them. Left: illustrati BRUSH PAINTING the situation.community and ‘mix’ from word association network. In thethe linkexample, Blend and blender belong tono ‘fruit juice’ Right: real examples community. In the bottom example, upper between appear and reappear does bo HAIR ruit juice’ communityother ‘mix’ community. they belong to several communities together. belong to any of the and communities, but In the bottom example, the COMB between appear and reappear does not ev link TOOTHBRUSH long to any of the other communities, but they belong to several communities together. HAIRSPRAY TOOTHPASTE link can simultaneously belong to multiple communities even though the link itself belongs to only
    35. 35. pping community structure around Acetyl-CoA in the E. coli metabolic network. Acetyl-CoA plays several tant roles in metabolism. Shown are only communities with homogeneity score equal to 1 (all compounds nity share at least one pathway annotation); all other links, including those that contribute to community Simple Complex ed. Pathway annotations shared by all community members are displayed with corresponding colors. The the right of Acetyl-CoA are grouped since they share the same exact pathway annotations. BROOM PAINT SWEEP PAINTER GROOM PAINTING BRUSH HAIR TOOTHBRUSH COMB HAIRSPRAY TOOTHPASTE Global • SUNSET, SUNRISE, ORANGE Local • SUNSET, SUNRISE, RED • SUNSET, SUNRISE, PRETTY, BEAUTIFUL • SUNSET, SUNRISE, MOON • SUNSET, SUNRISE, BEACH • SUNSET, SUNRISE, SUN, DAWN, DUSK, SUNSHINE • SUNSET, SUNRISE, DAWN, DUSK, AFTERNOON, EVENING
    36. 36. Then, how can we find hierarchical community structure in COMPLEX networks with pervasive overlap?
    37. 37. Our solution: Use Links
    38. 38. Our solution: Use Links
    39. 39. Our solution: Use Links “a group of densely interconnected nodes”
    40. 40. Our solution: Use Links “a group ofTopologically densely Similar interconnected nodes” LINKS
    41. 41. Colleagues Family Friends
    42. 42. Colleagues ‘Family’ links Family Friends
    43. 43. Colleagues ‘Family’ links Friends Family ‘Friends’ links
    44. 44. ‘Nerds & geeks’ links Colleagues ‘Family’ links Friends Family ‘Friends’ links
    45. 45. Nodes: multiple membership Links: unique membership
    46. 46. Overlap
    47. 47. Overlap
    48. 48. Hierarchy Communities
    49. 49. Hierarchy Communities
    50. 50. Reconciliation
    51. 51. So, How?
    52. 52. Similarity between links Hierarchical Clustering
    53. 53. Hierarchical Link Clustering (HLC)
    54. 54. A B ei k ejk c i k j a S(eac , ebc ) Figure S1: (A) The similarity measure S(eik , ejk ) between edges For this example, |n+ (i) ∪ n+ (j)| = 12 and |n+ (i) ∩ n+ (j)| = 4, cases: (B) an isolated (ka = kb = 1), connected triple (a,c,b) has S triangle has S = 1. structure can become radically different.) Thus, we neglect the ne first define the inclusive neighbors of a node i as:
    55. 55. A B ei k ejk c i k j a S(eac , ebc ) Figure S1: (A) The similarity measure S(eik , ejk ) between edges For this example, |n+ (i) ∪ n+ (j)| = 12 and |n+ (i) ∩ n+ (j)| = 4, cases: (B) an isolated (ka = kb = 1), connected triple (a,c,b) has S triangle has S = 1. 4 structure can become radically different.) Thus, we neglect12 ne the first define the inclusive neighbors of a node i as:
    56. 56. (a) 1 2 (c) 3 3!4 9 2!4 4 7 1!4 6 8 2!3 1!2 5 1!3 (b) 1 2 4!7 5!6 4!6 3 4!5 9 7!9 4 7 7!8 6 8!9 8 5 3!4 2!4 1!4 2!3 1!2 1!3 4!7 5!6 4!6 4!5 7!9 7!8 8!9
    57. 57. ?
    58. 58. Partition Density Community c has mc edges and nc induced nodes c mc nc
    59. 59. Partition Density Community c has mc edges and nc induced nodes c mc nc
    60. 60. Partition Density Community c has mc edges and nc induced nodes c mc nc mc = 8 nc = 5
    61. 61. Partition Density Community c has mc edges and nc induced nodes c mc nc = mc
    62. 62. Partition Density Community c has mc edges and nc induced nodes c mc nc − = mc − (nc − 1)
    63. 63. Partition Density Community c has mc edges and nc induced nodes c mc nc − mc − (nc − 1) = nc (nc −1) − 2 − (nc − 1)
    64. 64. Partition Density − mc − (nc − 1) = nc (nc −1) − 2 − (nc − 1) mc − (nc − 1) =2 (nc − 2)(nc − 1)
    65. 65. Partition Density − mc − (nc − 1) = nc (nc −1) − 2 − (nc − 1) mc − (nc − 1) =2 (nc − 2)(nc − 1) 2 mc − (nc − 1) D≡ mc M c (nc − 2)(nc − 1)
    66. 66. It’s just density No resolution limit
    67. 67. Boulatruelle Jondrette Brujon Anzelma Blacheville Dahlia Gueulemer Favourite MmeBurgon Fameuil Babet Child1 Zephine Eponine Listolier Child2 Montparnasse Tholomyes MotherPlutarch Claquesous Perpetue Fantine Mabeuf Marguerite Brevet Thenardier MmeThenardier Javert Combeferre Gavroche Simplice Champmathieu Judge Bahorel Courfeyrac Toussaint Chenildieu Joly Bamatabois Marius Enjolras Woman2 Cochepaille Grantaire Feuilly Cosette Valjean Bossuet Woman1 Gribier Prouvaire Magnon Fauchelevent MmeHucheloup LtGillenormand Scaufflaire MotherInnocent Gillenormand MlleBaptistine Gervais Pontmercy Isabeau BaronessT MlleGillenormand MmeDeR MmeMagloire CountessDeLo Labarre Myriel MmePontmercy Napoleon Geborand MlleVaubois OldMan Count Cravatte Champtercier 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
    68. 68. Does it really work?
    69. 69. Quantitative Evaluation Framework
    70. 70. Quantitative Evaluation Framework How homogeneous each Community quality community is? How accurate the # of Overlap quality overlap is? How many nodes are Community coverage covered? How many memberships Overlap coverage are assigned?
    71. 71. Quantitative Evaluation Framework How homogeneous each Community quality community is? How accurate the # of Overlap quality overlap is? How many nodes are Community coverage covered? How many memberships Overlap coverage are assigned?
    72. 72. Quantitative Evaluation Framework How homogeneous each Community quality community is? How accurate the # of Overlap quality overlap is? How many nodes are Community coverage covered? How many memberships Overlap coverage are assigned?
    73. 73. Quantitative Evaluation Framework How homogeneous each Community quality community is? How accurate the # of Overlap quality overlap is? How many nodes are Community coverage covered? How many memberships Overlap coverage are assigned?
    74. 74. Metadata Figure R11: Example of the network and available metadata for the Amazon.com product co-purchases network. Here we show a particular book (upper left), some of the books it is often bought with (lower left), the set of subjects it is classified into by Amazon.com (upper right), and the set of popular “tags” Amazon.com users have chosen to describe or annotate the book’s content (lower right). We can use shared tags to quantify how similar pairs of books are, and the more subjects a book has, the more communities it is expected to belong to. Other combinations of metadata are certainly possible. Other networks used here have analogous metadata.
    75. 75. Quantitative Evaluation Framework Community quality Amazon.com Community coverage no membership Subjects Subjects HIV / AIDS Medical Africa - General Africa Africa History Subjects HIV / AIDS Medical Nonfiction / General Infectious Diseases high coverage low coverage Overlap quality Metabolic network Overlap coverage community memberships Acetyl-CoA 1. Glycolysis / Gluconeogenesis 2. TCA cycle 3. Fatty acid biosynthesis 4. ... Many pathway Memberships high overlap IDP (Inosine diphosphate) 1. Purine metaboilsm Few pathway Memberships low overlap high overlap coverage low overlap coverage
    76. 76. and topologies (for example, the network range from sparse (average degree 6.34) to dense (average degree 38.95)). metadata network description N k community overlap PPI (Y2H) PPI network of S. cerevisiae 1647 3.06 Set of each protein’s The number of GO obtained by yeast two-hybrid known functions (GO terms (Y2H) experiment [3] terms)a PPI (AP/MS) Affinity purification mass 1004 16.57 GO terms GO terms spectrometry (AP/MS) experiment PPI (LC) Literature curated (LC) 1213 4.21 GO terms GO terms PPI (all) Union of Y2H, AP/MS, and LC 2729 8.92 GO terms GO-terms PPI networksb Metabolic Metabolic network (metabolites 1042 16.81 Set of each The number of connected by reactions) of E. metabolite’s pathway KEGG pathway coli annotations (KEGG)c annotations Phone Social contacts between mobile 885989 6.34 Each user’s most likely Call activity phone users [15, 16, 17] geographic location (number of phone callsd ) Actor Film actors that appear in the 67411 8.90 Set of plot keywords Length of career same movies during for all of the actor’s (year of first role) 2000–2009 [18] films US Congress Congressmen who co-sponsor 390 38.95 Political ideology, Seniority (number bills during the 108th US from the common of congresses Congress [19, 20] space score [21, 22] served) Philosopher Philosophers and their 1219 9.80 Set of (wikipedia) Number of philosophical influences, from hyperlinks exiting in wikipedia subject the English Wikipediae the philosopher’s page categories Word Assoc. English words that are often 5018 22.02 Set of each word’s Number of senses mentally associated [23] senses, as documented by WordNet f Amazon.com Products that users frequently 18142 5.09g Set of each product’s Number of product buy together user tags (annotations) categories
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
    78. 78. ,$-+.%$+ 2S89C;4(12S89;F8 1233Q<67R(12S89;F8 2S89C;4(PQ;C67R 1233Q<67R(PQ;C67R ,$"#)/+ - . / 0 - . / 0 N -6<O5 - . / 0 - . / 0 - - . / 0 ?29@(=5521% =3;>2<%123 .C6PQ8(A8912C;762< =1729 DE (.2<F9855 AB6C2524B89 . N !"#$%&'$"()%*+ / N /988@R(J2@QC;967R( 5)41-2&'$"()%*+ 0( N 0<:23;4 "*)! )!)'+ &#* )+)# $,')) ++%*+ "%*# &! %#" #%!* !%#*
    79. 79. d as soc. Wor ,$-+.%$+ 2S89C;4(12S89;F8 1233Q<67R(12S89;F8 2S89C;4(PQ;C67R 1233Q<67R(PQ;C67R ,$"#)/+ - . / 0 - . / 0 N -6<O5 - . / 0 - . / 0 - - . / 0 ?29@(=5521% =3;>2<%123 .C6PQ8(A8912C;762< =1729 DE (.2<F9855 AB6C2524B89 . N !"#$%&'$"()%*+ / N /988@R(J2@QC;967R( 5)41-2&'$"()%*+ 0( N 0<:23;4 "*)! )!)'+ &#* )+)# $,')) ++%*+ "%*# &! %#" #%!* !%#*
    80. 80. Examples
    81. 81. BROOM PAINT SWEEP PAINTER GROOM PAINTING BRUSH HAIR TOOTHBRUSH COMB HAIRSPRAY TOOTHPASTE
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
    83. 83. / 34(5&,-.."(46417&'8-"()&&'"$9!"#$&:8-.&;;<&='00> %&'()*+, !"#$% !"#$ &'"$(%5(-A(& 7"?"(46&-:&?-6@& !"#$%&'()&*#+# -#.# ,-./012
    84. 84. B proteasome core complex (GO:005839, C) threonine-type endopeptidase activity (GO:0004298, F) Signalosome (GO:0008180, C) ubiquitin-dependent protein catabolic process (GO:0006511, P) Protein deneddylation (GO:0000338, P) proteasome regulatory particle (GO:0005838, C) ubiquitin-dependent protein catabolic process (GO:0006511, P) endopeptidase activity (GO:0004175, F) Core Regulatory particle Proteasome ure S16: Another example of overlapping community structure. (A) The subnetwork
    85. 85. B 103 number of communities 103 metabolites ATP number of 2 10 ADP 2 H2O, H+ 10 1 Pi 10 0 10 101 0 50 100 150 200 number of communities per metabolite 0 E. coli 10 101 102 103 number of metabolites per community 106 mmunities 6 10 ber of users 105 105 4 10 104 10 3 102
    86. 86. u rren cies B 3 C number of communities 10 103 metabolites ATP number of 2 10 ADP 2 H2O, H+ 10 1 Pi 10 0 10 101 0 50 100 150 200 number of communities per metabolite 0 E. coli 10 101 102 103 number of metabolites per community 106 mmunities 6 10 ber of users 105 105 4 10 104 10 3 102
    87. 87. Hierarchical organization
    88. 88. ~600k nodes ~3M edges
    89. 89. threshold = 0.20
    90. 90. threshold = 0.20
    91. 91. threshold = 0.20
    92. 92. threshold = 0.20
    93. 93. threshold = 0.20
    94. 94. A B threshold = 0.23 50 km thr = 0.24 C D threshold thr = 0.27 = 0.20 thr = 0.27 F 0.4 0.5 0.6 0.7 0.8 E 0.9 1
    95. 95. Remaining hierarchy e 1 Phone Metabolic Word association 0.8 Q/Qmax 0.6 0.4 0.2 Actual Control 0 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 Link dendrogram threshold, t Figure 4 | Meaningful communities at multiple levels of the link dendrogram. a–c, The social network of mobile phone users displays co- located, overlapping communities on multiple scales. a, Heat map of the most likely locations of all users in the region, showing several cities. b, Cutting the dendrogram above the optimum threshold yields small, intra-
    96. 96. a b Planets Diving, Swim, Marine life SPLASH DUCK Water and aquatic animals MARSH Astronomy SAILING Astronomy MARS Scuba diving, DROWN SINKER DRIFT BOG SWAMP (more general terms) PLUTO URANUS Scuba diving Coral reef LAGOON SWAN CROCODILE SATURN GALAXY REEF SWIMMER EARTH UNDERWATER SAIL JUPITER OVERFLOW DIVER CORAL FLOAT POND REPTILE PLANET PLANETS NEPTUNE DIVING STARS MOAT UNIVERSE SNORKEL SWIM DUCKS VENUS DIVE RAFT ALLIGATOR ASTRONOMY SCUBA LAKE METEORITE ASTROLOGY CANOE PIER MOON MERMAID BROOK DOCK COMET FIN PADDLE CREEK METEOR STAR FLIPPER BAY FISHING OBSERVE UPSTREAM ASTEROID DOLPHIN RIVER CANAL ROCKET PORPOISE SKY ASTRONAUT Diving with animals OTTER FLOOD WHALE DOWNSTREAM SHUTTLE TELESCOPE SEAL TANK STREAM DAM SALMON MARINE FLOW WALRUS MAMMAL TROUT INLET c d SATURN MERMAID URANUS NEPTUNE DIVING JUPITER MARS SWIMMER PLUTO CORAL TELESCOPE VENUS SWIM STARS UNDERWATER FIN REEF MOON PLANETS SNORKEL MARINE GALAXY DIVE PLANET SCUBA METEOR UNIVERSE DOLPHIN DIVER ASTRONOMY FLIPPER ASTEROID METEORITE WHALE PORPOISE A community at threshold = 0.20, A community at threshold = 0.20, and sub-communities at threshold = 0.28 COMET and sub-communities at threshold = 0.28 WALRUS Figure 23: Examples of hierarchical structure in the word association network. The word association network is a nice example for this purpose, since it is easy to appreciate the meanings and contexts of the individual words and communities. (a) Here we pick a link and follow how the link merges with others as we climb the hierarchical tree. (b) We start from the link MARS–
    97. 97. Conclusion • Link viewpoint effectively removes the problem of overlap. • Global hierarchical structure can be found by clustering links. • doi:10.1038/nature09182 • http://barabasilab.neu.edu/projects/ linkcommunities/
    98. 98. Acknowledgements
    99. 99. Acknowledgements A.-L. Barabási, H. Yu, S. Ahnert, J. Park, D.- S. Lee, P.-J. Kim, M. A. Yildirim,
    100. 100. Acknowledgements A.-L. Barabási, H. Yu, S. Ahnert, J. Park, D.- S. Lee, P.-J. Kim, M. A. Yildirim, T. S. Evans, R. Lambiotte, Line Graphs, Link Partitions and Overlapping Communities, http://sites.google.com/site/linegraphs/
    101. 101. xkcd.com
    102. 102. a Spouses Alice and Bob also work together b Word Association examples Link communities COMBINE JOIN Alice FRUIT BLENDER INTEGRATE Bob JUICE BLEND MIX MIXTURE Family Work Node communities Alice Alice LOOK DISAPPEAR APPEAR VANISH Bob Bob SEE REAPPEAR Work Family SHOW ATTEND The Alice-Bob link was placed in family but both home and work relationships are identified ultiple relationships between nodes be found by link communities that assume one membe hemselves “inherit” multiple memberships from their links. Two nodes can belong to many c
    103. 103. link communities a Internal groups without distinguishing features are undetectable to ALL methods i e communities language class basketball team f d project g b prob. p a j c h students a b c d e f g h i j all students are identical one community, D = 0.750 b subtle structural differences are found by link communities g c coach e communities language class basketball team a f project prob. p i d j b h students a b c d e f g h i j coach coach separates them two communities, D = 0.756 c juniors basketball team seniors 1 2 3 4 5 6 7 8 9 10 21 22 23 24 25 26 27 28 29 30 6 10 1 3 11 12 13 14 15 16 17 18 19 20 14 2 20 7 project 24 12 prob. p 8 13 18 28 5 23 15 three communities, D = 0.745 4 17 25 9 26 11 16 Multiple relationships are found: 22 juniors and 19 29 The link between students 18 and 20 basketball players is senior but both 18 and 20 belong to 30 27 21 both seniors and basketball players! seniors and basketball players Figure 5: Some small, illustrative examples of the subtle structural changes that link communities detect, using the bipartite social model of [21] with p = 0.8, followed by our link communities algorithm. In (a) there are no distinguishing structural features to separate the “subsumed” basketball team from the language class. Detecting the team is impossible for all methods.
    1. A particular slide catching your eye?

      Clipping is a handy way to collect important slides you want to go back to later.

    ×