Background
RQ1: Has Barcelona en Comú preserved a decentralized structure or has it adopted a conventional centralized organization ruled by an elite?
RQ2: Does Barcelona en Comú discuss differently with other political parties than traditional parties do?
Methods
Community detection
N-Louvain method
Cluster characterization
Hierarchical structure
Small-world phenomenon
Coreness
Dataset
Political party | Party account(s) | Candidate account |
---|---|---|
@bcnencomu | ||
@icveuiabcn | ||
BeC | @podem_bcn | @adacolau |
@equobcn | ||
@pconstituentbcn | ||
CiU | @cdcbarcelona | @xaviertrias |
@uniobcn | ||
Cs | @cs_bcna | @carinamejias |
CUP | @capgirembcn | @mjlecha |
@cupbarcelona | ||
ERC | @ercbcn | @alfredbosch |
PP | @ppbarcelona_ | @albertofdezxbcn |
PSC | @pscbarcelona | @jaumecollboni |
Online party organization networks
Community detection
Cluster | User | PageRank | Role |
---|---|---|---|
BeC-p | @bcnencomu | 0.092 | Party |
BeC-p | @adacolau | 0.029 | Candidate |
BeC-p | @ahoramadrid | 0.009 | Allied party |
BeC-p | @ahorapodemos | 0.009 | Party |
BeC-p | @isaranjuez | 0.002 | Activist |
BeC-m | @toret | 0.014 | Activist |
BeC-m | @santidemajo | 0.005 | Activist |
BeC-m | @sentitcritic | 0.005 | Media |
BeC-m | @galapita | 0.005 | Activist |
BeC-m | @eloibadia | 0.005 | Activist |
Cs | @carinamejias | 0.007 | Candidate |
Cs | @cs_bcna | 0.006 | Party |
Cs | @ciudadanoscs | 0.004 | Party |
Cs | @soniasi02 | 0.003 | Activist |
Cs | @prensacs | 0.002 | Party |
CiU | @xaviertrias | 0.012 | Candidate |
CiU | @ciu | 0.004 | Party |
CiU | @bcn_ajuntament | 0.003 | Institution |
CiU | @cdcbarcelona | 0.002 | Party |
CiU | @uniobcn | 0.001 | Party |
CUP | @cupbarcelona | 0.016 | Party |
CUP | @capgirembcn | 0.008 | Party |
CUP | @albertmartnez | 0.005 | Media |
CUP | @mjlecha | 0.002 | Candidate |
CUP | @simongorjeos | 0.003 | Media |
ERC | @ercbcn | 0.016 | Party |
ERC | @alfredbosch | 0.011 | Candidate |
ERC | @arapolitica | 0.007 | Media |
ERC | @esquerra_erc | 0.004 | Party |
ERC | @directe | 0.003 | Media |
PP | @cati_bcn | 0.003 | Media |
PP | @albertofdezxbcn | 0.003 | Candidate |
PP | @maticatradio | 0.002 | Media |
PP | @ppbarcelona_ | 0.002 | Party |
PP | @carmenchusalas | 0.001 | Activist |
PSC | @pscbarcelona | 0.003 | Party |
PSC | @sergifor | 0.003 | Media |
PSC | @jaumecollboni | 0.002 | Candidate |
PSC | @elpaiscat | 0.002 | Media |
PSC | @annatorrasfont | 0.001 | Media |
User | Role |
\({\rm BeC \text{-}m ^{\rm{rt}}}\)
|
\({\rm BeC \text{-}p ^{\rm{rt}}}\)
|
\({\rm CiU ^{\rm{rt}}}\)
|
\({\rm Cs ^{\rm{rt}}}\)
|
\({\rm CUP ^{\rm{rt}}}\)
|
\({\rm ERC ^{\rm{rt}}}\)
|
\({\rm PP ^{\rm{rt}}}\)
|
\({\rm PSC ^{\rm{rt}}}\)
| Undef. |
---|---|---|---|---|---|---|---|---|---|---|
@btvnoticies | Media | 0 | 0 | 0 | 0 | 1 | 0 | 86 | 13 | 0 |
@elperiodico | Media | 0 | 90 | 0 | 3 | 0 | 1 | 0 | 1 | 5 |
@elsmatins | Media | 0 | 0 | 0 | 0 | 0 | 93 | 0 | 7 | 0 |
@naciodigital | Media | 0 | 0 | 1 | 0 |
38
|
61
| 0 | 0 | 0 |
@tv3cat | Media | 0 | 0 | 0 | 0 | 3 | 54 | 0 | 19 | 24 |
@encampanya | Media | 1 | 0 | 0 | 0 | 36 | 0 | 0 | 0 | 63 |
@rocsalafaixa | Citizen | 0 | 0 | 7 | 0 | 1 | 92 | 0 | 0 | 0 |
@bernatff | Media | 0 | 0 | 1 | 0 |
38
|
61
| 0 | 0 | 0 |
@jordi_palmer | Media | 0 | 0 | 1 | 0 |
38
|
61
| 0 | 0 | 0 |
@mariamariekke | Citizen |
50
|
50
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
@puntcattv3 | Media | 0 | 0 | 0 | 0 | 0 |
44
| 0 |
56
| 0 |
@ramontremosa | Politician | 0 | 0 | 90 | 0 | 0 | 10 | 0 | 0 | 0 |
@santimdx5 | Media | 91 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 9 |
@mtudela | Media | 0 | 0 | 7 | 0 | 1 | 92 | 0 | 0 | 0 |
@pah_bcn | Civic org | 89 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 11 |
@324cat | Media | 0 | 0 | 0 | 0 | 3 | 52 | 0 | 13 | 32 |
@terrassaencomu | Party | 2 | 92 | 0 | 0 | 0 | 0 | 0 | 0 | 6 |
@sicomtelevision | Media | 1 | 8 | 0 | 0 | 90 | 0 | 0 | 0 | 1 |
@xriusenoticies | Media | 0 | 0 |
35
| 0 | 0 | 0 | 0 |
65
| 0 |
@vagadetotes | Civic org |
78
| 0 | 0 | 0 |
22
| 0 | 0 | 0 | 0 |
Comparison to the Clique Percolation Method
-
All the nodes of the k-clique graphs related to CiU, Cs, CUP, ERC, and PSC are part of the corresponding clusters from the N-Louvain method.
-
Only one node from PP k-clique graph was not in PP political cluster.
-
The nodes from the k-clique graph related to a trade union of municipal police (\(\rm GU\)) were not in a political cluster.
-
The largest BeC k-clique graph (\(\rm BeC_1\)) is mainly formed by nodes from the BeC movement cluster. The smallest k-clique graph (\(\rm BeC_2\)) is composed of two nodes from the BeC party cluster and seven nodes from the BeC movement cluster.
CPM |
k
|
\(\text{BeC-m}^{\rm{rt}}\)
|
\(\text{BeC-p}^{\rm{rt}}\)
|
\(\text{CiU}^{\rm{rt}}\)
|
\(\text{Cs}^{\rm{rt}}\)
|
\(\text{CUP}^{\rm{rt}}\)
|
\(\text{ERC}^{\rm{rt}}\)
|
\(\text{PP}^{\rm{rt}}\)
|
\(\text{PSC}^{\rm{rt}}\)
| Undef. |
---|---|---|---|---|---|---|---|---|---|---|
\({\rm BeC_{1}}\)
| 9 |
60
| 3 | 0 | 0 | 0 | 0 | 0 | 0 | 2 |
\({\rm BeC_{2}}\)
| 9 |
7
| 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
CiU | 9 | 0 | 0 |
25
| 0 | 0 | 0 | 0 | 0 | 0 |
Cs | 9 | 0 | 0 | 0 |
10
| 0 | 0 | 0 | 0 | 0 |
CUP | 9 | 0 | 0 | 0 | 0 |
13
| 0 | 0 | 0 | 0 |
ERC | 7 | 0 | 0 | 0 | 0 | 0 |
7
| 0 | 0 | 0 |
PP | 9 | 0 | 0 | 0 | 0 | 0 | 0 |
20
| 0 | 1 |
PSC | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
18
| 0 |
GU | 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
11
|
-
The different size and structure of the political networks make that CPM at the maximum value of k only detects two major clusters. On the other hand, the new method is able to identify every party cluster.
-
The clusters obtained through CPM are k-cliques and, therefore, such clusters are dense graphs formed by the core of the party network structure. Social networks are characterized by their heavy-tailed degree distribution so the k-clique graphs exclude the large amount of less active users. Recent studies have proved that these are the nodes which compose the critical periphery in the growth of protest movements [6]. For this reason, the inclusion of these nodes, as the new method does, becomes essential for the following characterization of clusters.
Cluster characterization
Hierarchical structure
Cluster |
\(G_\mathrm{in}\)
|
\(C_\mathrm{in}\)
|
r
|
---|---|---|---|
\({\rm BeC \text{-}p ^{\rm{rt}}}\)
| 0.995 | 0.639 | 0.639 |
\({\rm Cs ^{\rm{rt}}}\)
| 0.964 | 0.476 | 0.480 |
\({\rm ERC ^{\rm{rt}}}\)
| 0.954 | 0.452 | 0.454 |
\({\rm CUP ^{\rm{rt}}}\)
| 0.953 | 0.635 | 0.636 |
\({\rm CiU ^{\rm{rt}}}\)
| 0.893 | 0.770 | 0.774 |
\({\rm PP ^{\rm{rt}}}\)
| 0.876 | 0.378 | 0.389 |
\({\rm PSC ^{\rm{rt}}}\)
| 0.818 | 0.565 | 0.578 |
\({\rm BeC \text{-}m ^{\rm{rt}}}\)
| 0.811 | 0.290 | 0.302 |
Small-world phenomenon
Cluster |
N
|
E
| Cl |
l
|
---|---|---|---|---|
\({\rm BeC \text{-}m ^{\rm{rt}}}\)
| 427 | 2431 | 0.208 | 3.35 |
\({\rm PP ^{\rm{rt}}}\)
| 301 | 1163 | 0.188 | 2.73 |
\({\rm PSC ^{\rm{rt}}}\)
| 211 | 810 | 0.182 | 2.29 |
\({\rm CiU ^{\rm{rt}}}\)
| 337 | 1003 | 0.114 | 4.66 |
\({\rm Cs ^{\rm{rt}}}\)
| 352 | 832 | 0.073 | 2.57 |
\({\rm CUP ^{\rm{rt}}}\)
| 635 | 1422 | 0.037 | 2.57 |
\({\rm ERC ^{\rm{rt}}}\)
| 866 | 1899 | 0.027 | 5.43 |
\({\rm BeC \text{-}p ^{\rm{rt}}}\)
| 1844 | 2427 | 0.002 | 2.48 |
Coreness
Cluster |
\(k_\mathrm{max}\)
|
\(k_\mathrm{avg}\)
|
---|---|---|
\({\rm BeC \text{-}m ^{\rm{rt}}}\)
| 17 | 5.90 (5.46) |
\({\rm PP ^{\rm{rt}}}\)
| 12 | 4.02 (3.99) |
\({\rm PSC ^{\rm{rt}}}\)
| 11 | 3.85 (3.55) |
\({\rm CiU ^{\rm{rt}}}\)
| 13 | 3.10 (3.44) |
\({\rm ERC ^{\rm{rt}}}\)
| 8 | 2.25 (1.85) |
\({\rm Cs ^{\rm{rt}}}\)
| 10 | 2.42 (2.42) |
\({\rm CUP ^{\rm{rt}}}\)
| 10 | 2.19 (2.22) |
\({\rm BeC \text{-}p ^{\rm{rt}}}\)
| 5 | 1.33 (0.71) |
Online party discussion networks
Community detection
Comparison to the network of retweets
Cluster |
\({\rm BeC \text{-}m ^{\rm{rt}}}\)
|
\({\rm BeC \text{-}p ^{\rm{rt}}}\)
|
\({\rm CiU ^{\rm{rt}}}\)
|
\({\rm Cs ^{\rm{rt}}}\)
|
\({\rm CUP ^{\rm{rt}}}\)
|
\({ \rm ERC ^{\rm{rt}}}\)
|
\({\rm PP ^{\rm{rt}}}\)
|
\({\rm PSC ^{\rm{rt}}}\)
| Undef. |
---|---|---|---|---|---|---|---|---|---|
\({ \rm BeC \text{-}c ^{\rm{rp}}}\)
| 37 |
140
| 13 | 1 | 14 | 47 | 6 | 3 | 3259 |
\({ \rm BeC \text{-}p ^{\rm{rp}}}\)
| 104 |
120
| 4 | 0 | 24 | 13 | 0 | 4 | 937 |
\({\rm CiU ^{\rm{rp}}}\)
| 27 | 48 |
108
| 6 | 37 | 17 | 13 | 13 | 1975 |
\({\rm Cs ^{\rm{rp}}}\)
| 2 | 18 | 0 |
100
| 5 | 16 | 12 | 1 | 925 |
\({\rm CUP ^{\rm{rp}}}\)
| 7 | 6 | 0 | 1 |
82
| 7 | 1 | 1 | 314 |
\({\rm ERC ^{\rm{rp}}}\)
| 1 | 6 | 7 | 2 | 9 |
113
| 0 | 2 | 519 |
\({\rm Ind ^{\rm{rp}}}\)
| 14 | 18 | 18 | 1 | 16 |
91
| 0 | 0 | 807 |
\({\rm Media \text{-}Cat ^{\rm{rp}}}\)
| 2 | 12 | 6 | 0 | 10 |
63
| 1 | 4 | 669 |
\({\rm Media \text{-}Spa ^{\rm{rp}}}\)
| 0 |
23
| 0 | 1 | 1 | 1 | 1 | 0 | 432 |
\({\rm Podemos ^{\rm{rp}}}\)
| 0 |
35
| 1 | 0 | 0 | 0 | 1 | 1 | 440 |
\({ \rm PP ^{\rm{rp}}}\)
| 2 | 5 | 5 | 4 | 4 | 6 |
80
| 4 | 435 |
\({\rm PSC ^{\rm{rp}}}\)
| 2 | 4 | 6 | 1 | 5 | 13 | 1 |
57
| 396 |
Cluster characterization
Cluster |
N
|
E
|
\(G_\mathrm{in}\)
| Cl |
l
|
\(k_\mathrm{max}\)
|
\(k_\mathrm{avg}\)
|
---|---|---|---|---|---|---|---|
\({\rm BeC \text{-}c ^{\rm{rp}}}\)
| 3520 | 3940 | 0.980 | 0.0001 | 3.28 | 3 | 1.11 (0.36) |
\({\rm BeC \text{-}p ^{\rm{rp}}}\)
| 1206 | 1624 | 0.908 | 0.0020 | 5.19 | 4 | 1.30 (0.64) |
\({\rm CiU ^{\rm{rp}}}\)
| 2244 | 3446 | 0.849 | 0.0009 | 2.72 | 4 | 1.30 (0.60) |
\({\rm Cs ^{\rm{rp}}}\)
| 1079 | 1478 | 0.900 | 0.0044 | 3.48 | 4 | 1.31 (0.67) |
\({\rm CUP ^{\rm{rp}}}\)
| 419 | 528 | 0.865 | 0.0052 | 5.25 | 3 | 1.22 (0.49) |
\({\rm ERC ^{\rm{rp}}}\)
| 659 | 841 | 0.927 | 0.0032 | 3.36 | 3 | 1.24 (0.51) |
\({\rm Ind ^{\rm{rp}}}\)
| 965 | 1789 | 0.724 | 0.0333 | 5.37 | 5 | 1.58 (0.98) |
\({\rm Media \text{-}Cat ^{\rm{rp}}}\)
| 767 | 1055 | 0.899 | 0.0076 | 3.57 | 4 | 1.35 (0.73) |
\({\rm Media \text{-}Spa ^{\rm{rp}}}\)
| 459 | 499 | 0.974 | 0.0011 | 1.35 | 2 | 1.10 (0.31) |
\({\rm Podemos ^{\rm{rp}}}\)
| 478 | 549 | 0.951 | 0.0013 | 1.79 | 2 | 1.12 (0.32) |
\({\rm PP ^{\rm{rp}}}\)
| 545 | 709 | 0.876 | 0.0104 | 3.26 | 3 | 1.27 (0.55) |
\({\rm PSC ^{\rm{rp}}}\)
| 485 | 614 | 0.892 | 0.0032 | 2.94 | 3 | 1.23 (0.49) |
Discussion
Institutionalization of a movement
Discussion behaviors
Contribution of our methodology
-
Hierarchical structure In-degree centralization [22] was originally applied in [23] to measure the hierarchical structure of a network. This metric is based on (1) how the centrality of the most central node exceeds the centrality of all other nodes and (2) the comparison to a star network. Maximum and average in-degree have common differences of several orders of magnitude in social graphs. Therefore, in-degree centralization is approximately equal to the ratio between the maximum in-degree and the number of nodes for social networks with a heavy-tailed in-degree distribution. In other words, the in-degree centralization is not a good metric to capture hierarchical structure for social diffusion graphs, and the Gini coefficient for in-degree inequality represents a more reliable measure of the hierarchical structure of a network.
-
Information efficiency Information efficiency in social networks is closely related to the small-world phenomenon. This article uses the average path length, as the previous framework does [23], and the clustering coefficient to better characterize efficiency in social networks.
-
Social resilience Previous studies indicated the suitability of the k-core decomposition to measure the resilience of social networks [24]. This framework recommends the term coreness which represents a more precise definition of this metric. In addition, showing the distribution of nodes along k-cores does capture resilience better than maximum k-core as done in [23].