Core of communities in bipartite networks

Christian Bongiorno, András London, Salvatore Miccichè, and Rosario N. Mantegna

Phys. Rev. E 96, 022321 – Published 25 August 2017

Abstract

We use the information present in a bipartite network to detect cores of communities of each set of the bipartite system. Cores of communities are found by investigating statistically validated projected networks obtained using information present in the bipartite network. Cores of communities are highly informative and robust with respect to the presence of errors or missing entries in the bipartite network. We assess the statistical robustness of cores by investigating an artificial benchmark network, the coauthorship network, and the actor-movie network. The accuracy and precision of the partition obtained with respect to the reference partition are measured in terms of the adjusted Rand index and the adjusted Wallace index, respectively. The detection of cores is highly precise, although the accuracy of the methodology can be limited in some cases.

Received 6 March 2017

DOI:https://doi.org/10.1103/PhysRevE.96.022321

Physics Subject Headings (PhySH)

Community structure

Networks

Authors & Affiliations

Christian Bongiorno¹, András London², Salvatore Miccichè¹, and Rosario N. Mantegna^1,3,4

¹Dipartimento di Fisica e Chimica, Università degli Studi di Palermo, Viale delle Scienze Ed. 18, I-90128 Palermo, Italy
²Institute of Informatics, University of Szeged, Árpád tér 2, H-6720 Szeged, Hungary
³Center for Network Science, Central European University, Nador 9, H-1051 Budapest, Hungary
⁴Department of Computer Science, University College London, Gower Street, London WC1E 6BT, United Kingdom

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 96, Iss. 2 — August 2017

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Bipartite artificial benchmark network obtained with $q = 5, S_{A} = 5, S_{B} = 16$ , and $p_{c} = 1$ . Nodes in the bottom (top) row belongs to set $A$ ( $B$ ). (b) Network projection for the nodes of set $A$ of the artificial benchmark of panel (a). (c) Bipartite artificial benchmark with $q = 5, S_{A} = 5, S_{B} = 16, p_{c} = 1$ , and $p_{r} = 0.2$ .
Reuse & Permissions
Figure 2
Three examples of a comparison of a reference partition (membership of nodes indicated by their position in different boxes) with a considered partition (membership of nodes indicated by different colors and shape). In the example, a system of 116 nodes has four communities of different size in the reference partition (see four boxes with 64, 24, 16, and 12 nodes) and eight communities of different size in the considered partition. This second partition is indicated by the colors and shape of nodes. We have groups of light gray stars (32 nodes), maroon up-triangles (18), orange squares (16), purple down-triangles (16), red circles (16), yellow diamonds (9), green left-triangles (6), and blue crosses (3). In the three examples, $W_{adj}$ assumes the following values: (top panel) $W_{adj} = 1.0$ , (middle panel) $W_{adj} = 0.88$ , and (bottom panel) $W_{adj} = 0.03$ .
Reuse & Permissions
Figure 3
$R_{adj}$ and $W_{adj}$ measured between the partition obtained by performing community detection for the three types of projected networks: (i) Full (green circles), (ii) FDR (red diamonds), and (iii) Bonferroni (blue crosses), and the reference partition of the artificial benchmark. The benchmark has the parameters $S_{A} = 50, S_{B} = 50, p_{c} = 0.8$ , and $q = 50$ . Simulations and community detection are performed for several values of $p_{r}$ ranging from 0.3 to 0.9 in steps of 0.025. Average value and one standard deviation error bar are obtained by performing the analysis on 10 different realizations.
Reuse & Permissions
Figure 4
$R_{adj}$ and $W_{adj}$ measured between the partition obtained by performing community detection for the three types of projected networks: (i) Full (green circles), (ii) FDR (red diamonds), and (iii) Bonferroni (blue crosses), and the reference partition of the artificial benchmark. The benchmark has the parameters $S_{A} = 50, S_{B} = 50, p_{r} = 0.6$ , and $q = 50$ . Simulations and community detection are performed for several values of $p_{c}$ ranging from 0 to 1.0 in steps of 0.025. The average value and one standard deviation error bar are obtained by performing the analysis on 10 different realizations.
Reuse & Permissions
Figure 5
Coauthorship database. (a) Average $R_{adj}$ value between 100 partitions of the Full network (green circles), the Bonferroni SVN (blue crosses), and FDR SVN (red diamonds) obtained as different stochastic realizations for each investigated value of $p_{r}$ and the best partition $G 0$ obtained in the absence of additional noise. The error bar indicates one standard deviation. (b) Average $W_{adj}$ of the same partitions.
Reuse & Permissions
Figure 6
IMDB database. Time period 1990–1994. (a) Average $R_{adj}$ value between 100 partitions of the Full network (green circles), the Bonferroni SVN (blue crosses), and FDR SVN (red diamonds) obtained as different stochastic realizations for each investigated value of $p_{r}$ and the best partition $G 0$ obtained in the absence of additional noise. The error bar indicates one standard deviation. (b) Average $W_{adj}$ of the same partitions.
Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics