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Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 01 + 2024 + + + 9 + + 93 + + + + netroles: A Java library for role equivalence analysis +in networks + + + + Julian + Müller + https://orcid.org/0000-0001-6440-8046 + + + + 01 + 17 + 2024 + + + 5903 + + + 10.21105/joss.05903 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.10070537 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/5903 + + + + 10.21105/joss.05903 + https://joss.theoj.org/papers/10.21105/joss.05903 + + + https://joss.theoj.org/papers/10.21105/joss.05903.pdf + + + + + + dBlockmodeling: Deterministic blockmodeling +of signed, one-mode and two-mode networks + Brusco + 2023 + Brusco, M. (2023). dBlockmodeling: +Deterministic blockmodeling of signed, one-mode and two-mode networks. +https://CRAN.R-project.org/package=dBlockmodeling + + + Social network analysis with +sna + Butts + Journal of Statistical +Software + 6 + 24 + 10.18637/jss.v024.i06 + 1548-7660 + 2008 + Butts, C. T. (2008). Social network +analysis with sna. Journal of Statistical Software, 24(6). +https://doi.org/10.18637/jss.v024.i06 + + + visone software for visual social network +analysis + Baur + Graph Drawing. 9th International Symposium, +GD 2001 + 10.1007/3-540-45848-4_47 + 2002 + Baur, M., Benkert, M., Brandes, U., +Cornelsen, S., Gaertler, M., Köpf, B., Lerner, J., & Wagner, D. +(2002). visone software for visual social network analysis. In P. +Mutzel, M. Jünger, & S. Leipert (Eds.), Graph Drawing. 9th +International Symposium, GD 2001 (pp. 463–464). Springer. +https://doi.org/10.1007/3-540-45848-4_47 + + + Deterministic blockmodelling of signed and +two-mode networks: A tutorial with software and psychological +examples + Brusco + British Journal of Mathematical and +Statistical Psychology + 1 + 74 + 10.1111/bmsp.12192 + 0007-1102 + 2021 + Brusco, M., Doreian, P., & +Steinley, D. (2021). Deterministic blockmodelling of signed and two-mode +networks: A tutorial with software and psychological examples. British +Journal of Mathematical and Statistical Psychology, 74(1), 34–63. +https://doi.org/10.1111/bmsp.12192 + + + Ecological and perfect +colorings + Borgatti + Social Networks + 1 + 16 + 10.1016/0378-8733(94)90010-8 + 1994 + Borgatti, S. P., & Everett, M. G. +(1994). Ecological and perfect colorings. Social Networks, 16(1), 43–55. +https://doi.org/10.1016/0378-8733(94)90010-8 + + + Graph colorings and power in experimental +exchange networks + Borgatti + Social Networks + 3-4 + 14 + 10.1016/0378-8733(92)90006-S + 1992 + Borgatti, S. P., & Everett, M. G. +(1992). Graph colorings and power in experimental exchange networks. +Social Networks, 14(3-4), 287–308. +https://doi.org/10.1016/0378-8733(92)90006-S + + + Notions of position in social network +analysis + Borgatti + Sociological Methodology + 22 + 10.2307/270991 + 1992 + Borgatti, S. P., & Everett, M. G. +(1992). Notions of position in social network analysis. Sociological +Methodology, 22, 1–35. +https://doi.org/10.2307/270991 + + + UCINET for Windows: Software for social +network analysis + Borgatti + 2002 + Borgatti, S. P., Everett, M. G., +& Freeman, L. C. (2002). UCINET for Windows: Software for social +network analysis. Analytic Technologies. + + + Pajek analysis and visualization of large +networks + Batagelj + Graph Drawing Software + 10.1007/978-3-642-18638-7_4 + 2004 + Batagelj, V., & Mrvar, A. (2004). +Pajek analysis and visualization of large networks. In M. Jünger & +P. Mutzel (Eds.), Graph Drawing Software (pp. 77–103). Springer. +https://doi.org/10.1007/978-3-642-18638-7_4 + + + visone analysis and visualization of social +networks + Brandes + Graph Drawing Software + 10.1007/978-3-642-18638-7_15 + 2004 + Brandes, U., & Wagner, D. (2004). +visone analysis and visualization of social networks. In M. Jünger & +P. Mutzel (Eds.), Graph Drawing Software (pp. 321–340). Springer. +https://doi.org/10.1007/978-3-642-18638-7_15 + + + sbm: Stochastic blockmodels + Chiquet + 2023 + Chiquet, J., Donnet, S., & +Barbillon, P. (2023). sbm: Stochastic blockmodels. +https://CRAN.R-project.org/package=sbm + + + Exact colorations of graphs and +digraphs + Everett + Social Networks + 4 + 18 + 10.1016/0378-8733(95)00286-3 + 1996 + Everett, M. G., & Borgatti, S. P. +(1996). Exact colorations of graphs and digraphs. Social Networks, +18(4), 319–331. +https://doi.org/10.1016/0378-8733(95)00286-3 + + + Ego-centered and local roles: A graph +theoretic approach + Everett + The Journal of Mathematical +Sociology + 3-4 + 15 + 10.1080/0022250X.1990.9990067 + 0022-250X + 1990 + Everett, M. G., Boyd, J. P., & +Borgatti, S. P. (1990). Ego-centered and local roles: A graph theoretic +approach. The Journal of Mathematical Sociology, 15(3-4), 163–172. +https://doi.org/10.1080/0022250X.1990.9990067 + + + The study of man: An +introduction + Linton + 1936 + Linton, R. (1936). The study of man: +An introduction. Appleton-Century. + + + blockmodels: Latent and stochastic block +model estimation by a ’V-EM’ algorithm + Leger + 2021 + Leger, J.-B., Barbillon, P., & +Chiquet, J. (2021). blockmodels: Latent and stochastic block model +estimation by a ’V-EM’ algorithm. +https://CRAN.R-project.org/package=blockmodels + + + Structural equivalence of individuals in +social networks + Lorrain + The Journal of Mathematical +Sociology + 1 + 1 + 10.1080/0022250X.1971.9989788 + 0022-250X + 1971 + Lorrain, F., & White, H. C. +(1971). Structural equivalence of individuals in social networks. The +Journal of Mathematical Sociology, 1(1), 49–80. +https://doi.org/10.1080/0022250X.1971.9989788 + + + Social theory and social +structure + Merton + 1957 + Merton, R. K. (1957). Social theory +and social structure. Free Press. + + + The evolution of roles + Müller + Social Networks + 68 + 10.1016/j.socnet.2021.02.001 + 2022 + Müller, J., & Brandes, U. (2022). +The evolution of roles. Social Networks, 68, 195–208. +https://doi.org/10.1016/j.socnet.2021.02.001 + + + dynsbm: Dynamic stochastic block +models + Matias + 2020 + Matias, C., & Miele, V. (2020). +dynsbm: Dynamic stochastic block models. +https://CRAN.R-project.org/package=dynsbm + + + The theory of social structure + Nadel + 1957 + Nadel, S. F. (1957). The theory of +social structure. Free Press. + + + The graph-tool python library + Peixoto + figshare + 10.6084/m9.figshare.1164194 + 2014 + Peixoto, T. P. (2014). The graph-tool +python library. Figshare. +https://doi.org/10.6084/m9.figshare.1164194 + + + signnet: An R package for analyzing signed +networks + Schoch + Journal of Open Source +Software + 81 + 8 + 10.21105/joss.04987 + 2475-9066 + 2023 + Schoch, D. (2023). signnet: An R +package for analyzing signed networks. Journal of Open Source Software, +8(81), 4987. https://doi.org/10.21105/joss.04987 + + + Stochastic blockmodeling of linked +networks + Škulj + Social Networks + 70 + 10.1016/j.socnet.2022.02.001 + 2022 + Škulj, D., & Žiberna, A. (2022). +Stochastic blockmodeling of linked networks. Social Networks, 70, +240–252. +https://doi.org/10.1016/j.socnet.2022.02.001 + + + Roles and positions: A critique and extension +of the blockmodeling approach + Winship + Sociological Methodology + 14 + 10.2307/270911 + 1983 + Winship, C., & Mandel, M. (1983). +Roles and positions: A critique and extension of the blockmodeling +approach. Sociological Methodology, 14, 314–344. +https://doi.org/10.2307/270911 + + + Graph and semigroup homomorphisms on networks +of relations + White + Social Networks + 2 + 5 + 10.1016/0378-8733(83)90025-4 + 1983 + White, D. R., & Reitz, K. P. +(1983). Graph and semigroup homomorphisms on networks of relations. +Social Networks, 5(2), 193–234. +https://doi.org/10.1016/0378-8733(83)90025-4 + + + Generalized blockmodeling of valued +networks + Žiberna + Social Networks + 1 + 29 + 10.1016/j.socnet.2006.04.002 + 2007 + Žiberna, A. (2007). Generalized +blockmodeling of valued networks. Social Networks, 29(1), 105–126. +https://doi.org/10.1016/j.socnet.2006.04.002 + + + Generalized and classical blockmodeling of +valued networks + Žiberna + 2023 + Žiberna, A., & Cugmas, M. (2023). +Generalized and classical blockmodeling of valued networks. +https://CRAN.R-project.org/package=blockmodeling + + + Stochastic blockmodeling of one-mode and +linked networks + Žiberna + 2023 + Žiberna, A., & Telarico, F. A. +(2023). Stochastic blockmodeling of one-mode and linked networks. +https://CRAN.R-project.org/package=StochBlock + + + + + + From 7b8950c692d8e47e27810f26cd1c4a274e68eaf8 Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Wed, 17 Jan 2024 17:47:48 +0000 Subject: [PATCH 3/4] Creating 10.21105.joss.05903.jats --- joss.05903/10.21105.joss.05903.jats | 797 ++++++++++++++++++++++++++++ 1 file changed, 797 insertions(+) create mode 100644 joss.05903/10.21105.joss.05903.jats diff --git a/joss.05903/10.21105.joss.05903.jats b/joss.05903/10.21105.joss.05903.jats new file mode 100644 index 0000000000..6351f6b77e --- /dev/null +++ b/joss.05903/10.21105.joss.05903.jats @@ -0,0 +1,797 @@ + + +

+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +5903 +10.21105/joss.05903 + +netroles: A Java library for role equivalence analysis in +networks + + + +https://orcid.org/0000-0001-6440-8046 + +Müller +Julian + + + + + + +Social Networks Lab, ETH Zürich, Switzerland + + + + +Institute of Computing, Università della Svizzera italiana, +Switzerland + + + + +29 +8 +2023 + +9 +93 +5903 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Java +network analysis +role analysis + + + + + + Summary +

An important problem in the analysis of networks is structural + similarity. It has commonly been expressed in terms of role + equivalences, which have often been considered to formalize the + concepts of social role and position as discussed by Linton + (1936), + Merton + (1957) and + Nadel + (1957) in + their analyses of social structure + (Borgatti + & Everett, 1992a). Role equivalences are based on the idea + that actors are equivalent or play the same role if they form ties to + similar others in similar ways. For example, the role of “doctor” is + characterized by a set of ties to others playing related roles like + “nurses”, “patients” and “colleagues”. However, this equivalence idea + has been interpreted by different authors in different ways, resulting + in the proposition of diverse definitions of role equivalence such as + structural + (Lorrain + & White, 1971) or regular equivalence + (White + & Reitz, 1983). The netroles library + provides implementations of many established notions of role + equivalence, but more importantly, it offers a unified approach to + role equivalence analysis that generalizes beyond the classic role + equivalences, allowing users to express more complex kinds of role + notions suitable for networks with multiple relations and + attributes.

+
+ + Statement of need +

The general-purpose network analysis software + UCINET + (Borgatti + et al., 2002), visone + (Baur + et al., 2002; + Brandes + & Wagner, 2004), and the R package + sna + (Butts, + 2008) provide some methods to compute structural, regular, or + regular equitable + (Everett + & Borgatti, 1996) equivalence as specific notions of role. + More wide-spread are software tools that implement two kinds of + relaxations of role equivalence:

+ + +

Distance or similarity measures based on structural, regular, + or equitable equivalence are offered by software such as + blockmodeling + (Žiberna + & Cugmas, 2023), Pajek + (Batagelj + & Mrvar, 2004), sna + (Butts, + 2008), and UCINET + (Borgatti + et al., 2002).

+
+ +

Blockmodeling aims to find equivalences that + best globally approximate a notion of role equivalence on a given + network. Software like graph-tool + (Peixoto, + 2014), sbm + (Chiquet + et al., 2023), blockmodels + (Leger + et al., 2021), StochBlock + (Škulj + & Žiberna, 2022; + Žiberna + & Telarico, 2023), and dynsbm + (Matias + & Miele, 2020) offer stochastic + blockmodeling methods derived from stochastic versions of + structural equivalence. Packages such as + blockmodeling + (Žiberna, + 2007; + Žiberna + & Cugmas, 2023), dBlockmodeling + (Brusco + et al., 2021; + Brusco, + 2023), Pajek + (Batagelj + & Mrvar, 2004), and signnet + (Schoch, + 2023) implement optimizational + blockmodeling minimizing some criterion function based on + one or more role equivalence concepts.

+
+
+

Nonetheless, only few tools offer partial support to compute a + small selection of non-relaxed role equivalences, yet these solutions + do not generalize to other kinds of role equivalences and are + restricted to specific kinds of networks, such as unweighted networks + or networks with categorical tie weights.

+

The netroles library is intended to close + this gap and aims to extend the aim of applicability of role + equivalences. It provides a unified framework for role equivalences + based on the formalization of role equivalence proposed in Müller + & Brandes + (2022). The + library implements established notions of role, but its main goal is + to enable the expression of new role concepts, incorporating vertex + and edge attributes as well as multiple relations according to the + requirements of the network study. This also facilities the + specification of error-tolerant role equivalences that allow for minor + deviations from the ideal case. The example analyses in Müller & + Brandes + (2022) were + conducted using netroles.

+
+ + Background +

The conceptual idea of role equivalence can be restated as a + matching problem: two vertices + + i + and + + j + are role-equivalent if all neighbors or incident edges of + + + i + can be matched with neighbors or incident edges of + + + j + according to some set of matching rules and vice versa. These matching + rules, in turn, frequently depend on some equivalence among the + neighbors. Put differently, this defines an operation “relative role + equivalence” that produces an equivalence by applying the matching + rules relative to some given equivalence. Müller & Brandes + (2022) + showed that established role equivalences can be obtained as fixed + points of relative role equivalence and the derived operations “role + restriction” and “role extension”, if suitable matching rules are + chosen. The table below arranges established role equivalences + supported by netroles by the underlying + matching rules and the operations they are fixed points of.

+ + +

Established role equivalences as fixed points of the operations + relative role equivalence, role restriction and role extension by + type of matching rules.

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
matching typematching rules for comparing + + + i + and + + jrelative role equiv.role restrictionrole extension
weakno restrictionsweak equiv. + (Winship + & Mandel, 1983)refinements of weak equiv.coarsenings of weak equiv.
weakly equitableeach edge matches at most oncedegree equalityrefinements of degree equal.coarsenings of degree equal.
strong structuralsame neighborsstructural equiv. + (Lorrain + & White, 1971)refinements of struct. equiv.coarsenings of struct. equiv.
weak structuraltie + + (i,j) + matched with tie + + (j,i) + and + + (i,i) + with + + (j,j), + else same neighborsweak structural equiv. + (Everett + et al., 1990)refinements of weak struct. equiv.coarsenings of weak struct. equiv.
regularequivalent neighborsperfect equiv. + (Borgatti + & Everett, 1994)regular equiv. + (White + & Reitz, 1983)ecological equiv. + (Borgatti + & Everett, 1992b)
equitableequivalent neighbors, each edge matches at most onceequitable perfect equiv. + (Everett + & Borgatti, 1996)equitable regular equiv. + (Everett + & Borgatti, 1996)equitable ecological equiv. + (Everett + & Borgatti, 1996)
+
+
+ + Design +

The netroles library enables users to + specify the relative role equivalence operation as appropriate. + Inspired by dataflow and functional programming paradigms, users can + define the relative role equivalence operation through composition of + simple operators in a declarative style. All other role operations + described in Müller & Brandes + (2022) are + derived automatically. The focus on composition greatly increases the + library’s expressive power and improves its extensibility, as complex + scenarios can be handled by breaking down the role definition into + simpler suboperations.

+

To demonstrate this compositional design, we define an + error-tolerant version of equitable equivalence, which considers two + vertices role-equivalent if there is at most one deviation from the + underlying matching rules for outgoing edges in each direction of + comparison, as long as the compared vertices are not isolates. The + resulting binary relation is transitively closed to regain an + equivalence. The example in Section 5 of Müller & Brandes + (2022) is + based on this error-tolerant equivalence.

+

The dataflow diagram below describes this role operator + graphically. Note that some intermediate results are not + equivalences.

+ +

Dataflow diagram of error-tolerant role + operator

+ +
+

The following code expresses this role operator using + netroles:

+ RoleOperator<ConstMapping.OfInt> errortolerantOp = Operators.parallel( + Reducers.EQUIVALENCE.meet(), // combine by intersecting equivalences + Operators.composeRoleOp( + Operators.composeOp( + Operators.composeOp( + // threshold pairwise deviations from equitable equivalence by one + DistanceOperators.EQUIVALENCE.equitable() + .of(NetworkView.fromNetworkRelation(network, Direction.OUTGOING)) + .make(), + Converters.thresholdDistances((i, j) -> 1)), + // symmetrize (at most one deviation in each directions) + RoleOperators.BINARYRELATION.basic().symmetrize()), + // close over pairs of role-equivalent vertices transitively + Converters.strongComponentsAsEquivalence()), + // and separate isolates + RoleOperators.EQUIVALENCE.weak() + .of(n, NetworkView.fromNetworkRelation(network, Direction.OUTGOING)) + .make()); +
+ + + + + + + BruscoMichael + + dBlockmodeling: Deterministic blockmodeling of signed, one-mode and two-mode networks + 2023 + https://CRAN.R-project.org/package=dBlockmodeling + + + + + + ButtsCarter T. + + Social network analysis with sna + Journal of Statistical Software + 2008 + 24 + 6 + 1548-7660 + 10.18637/jss.v024.i06 + + + + + + BaurMichael + BenkertMarc + BrandesUlrik + CornelsenSabine + GaertlerMarco + KöpfBoris + LernerJürgen + WagnerDorothea + + visone software for visual social network analysis + Graph Drawing. 9th International Symposium, GD 2001 + + MutzelPetra + JüngerMichael + LeipertSebastian + + Springer + Berlin, Heidelberg + 2002 + 10.1007/3-540-45848-4_47 + 463 + 464 + + + + + + BruscoMichael + DoreianPatrick + SteinleyDouglas + + Deterministic blockmodelling of signed and two-mode networks: A tutorial with software and psychological examples + British Journal of Mathematical and Statistical Psychology + 202102 + 74 + 1 + 0007-1102 + 10.1111/bmsp.12192 + 34 + 63 + + + + + + BorgattiStephen P. + EverettMartin G. + + Ecological and perfect colorings + Social Networks + 199401 + 16 + 1 + 10.1016/0378-8733(94)90010-8 + 43 + 55 + + + + + + BorgattiStephen P. + EverettMartin G. + + Graph colorings and power in experimental exchange networks + Social Networks + 199209 + 14 + 3-4 + 10.1016/0378-8733(92)90006-S + 287 + 308 + + + + + + BorgattiStephen P. + EverettMartin G. + + Notions of position in social network analysis + Sociological Methodology + 1992 + 22 + https://www.jstor.org/stable/270991 + 10.2307/270991 + 1 + 35 + + + + + + BorgattiStephen P. + EverettMartin G. + FreemanLinton C. + + UCINET for Windows: Software for social network analysis + Analytic Technologies + Harvard + 2002 + + + + + + BatageljVladimir + MrvarAndrej + + Pajek analysis and visualization of large networks + Graph Drawing Software + + JüngerMichael + MutzelPetra + + Springer + Berlin, Heidelberg + 2004 + 10.1007/978-3-642-18638-7_4 + 77 + 103 + + + + + + BrandesUlrik + WagnerDorothea + + visone analysis and visualization of social networks + Graph Drawing Software + + JüngerMichael + MutzelPetra + + Springer + Berlin, Heidelberg + 2004 + 10.1007/978-3-642-18638-7_15 + 321 + 340 + + + + + + ChiquetJulien + DonnetSophie + BarbillonPierre + + sbm: Stochastic blockmodels + 2023 + https://CRAN.R-project.org/package=sbm + + + + + + EverettMartin G. + BorgattiStephen P. + + Exact colorations of graphs and digraphs + Social Networks + 199610 + 18 + 4 + 10.1016/0378-8733(95)00286-3 + 319 + 331 + + + + + + EverettMartin G. + BoydJohn P. + BorgattiStephen P. + + Ego-centered and local roles: A graph theoretic approach + The Journal of Mathematical Sociology + 199001 + 15 + 3-4 + 0022-250X + 10.1080/0022250X.1990.9990067 + 163 + 172 + + + + + + LintonRalph + + The study of man: An introduction + Appleton-Century + 1936 + + + + + + LegerJean-Benoist + BarbillonPierre + ChiquetJulien + + blockmodels: Latent and stochastic block model estimation by a ’V-EM’ algorithm + 2021 + https://CRAN.R-project.org/package=blockmodels + + + + + + LorrainFrançois + WhiteHarrison C. + + Structural equivalence of individuals in social networks + The Journal of Mathematical Sociology + 197101 + 1 + 1 + 0022-250X + 10.1080/0022250X.1971.9989788 + 49 + 80 + + + + + + MertonRobert King + + Social theory and social structure + Free Press + 1957 + + + + + + MüllerJulian + BrandesUlrik + + The evolution of roles + Social Networks + 202201 + 68 + 10.1016/j.socnet.2021.02.001 + 195 + 208 + + + + + + MatiasCatherine + MieleVincent + + dynsbm: Dynamic stochastic block models + 2020 + https://CRAN.R-project.org/package=dynsbm + + + + + + NadelSiegfried Frederick + + The theory of social structure + Free Press + 1957 + + + + + + PeixotoTiago P. + + The graph-tool python library + figshare + 2014 + 10.6084/m9.figshare.1164194 + + + + + + SchochDavid + + signnet: An R package for analyzing signed networks + Journal of Open Source Software + 202301 + 8 + 81 + 2475-9066 + 10.21105/joss.04987 + 4987 + + + + + + + ŠkuljDamjan + ŽibernaAleš + + Stochastic blockmodeling of linked networks + Social Networks + 202207 + 70 + 10.1016/j.socnet.2022.02.001 + 240 + 252 + + + + + + WinshipChristopher + MandelMichael + + Roles and positions: A critique and extension of the blockmodeling approach + Sociological Methodology + 1983 + 14 + https://www.jstor.org/stable/270911 + 10.2307/270911 + 314 + 344 + + + + + + WhiteDouglas R. + ReitzKarl P. + + Graph and semigroup homomorphisms on networks of relations + Social Networks + 198306 + 5 + 2 + 10.1016/0378-8733(83)90025-4 + 193 + 234 + + + + + + ŽibernaAleš + + Generalized blockmodeling of valued networks + Social Networks + 200701 + 29 + 1 + 10.1016/j.socnet.2006.04.002 + 105 + 126 + + + + + + ŽibernaAleš + CugmasMarjan + + Generalized and classical blockmodeling of valued networks + 2023 + https://CRAN.R-project.org/package=blockmodeling + + + + + + ŽibernaAleš + TelaricoFabio Ashtar + + Stochastic blockmodeling of one-mode and linked networks + 2023 + https://CRAN.R-project.org/package=StochBlock + + + + +
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