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Geodesic Cycle Length Distributions in Delusional and Other Social Networks

Journal of Social Structure
Volume 21 (2020): Issue 1 (January 2020)
By:
Open Access
|Oct 2020

Figures & Tables

Figure 1:

This graph has seven cycles (one is Hamiltonian). Four are chordless and three of those are also geodesic (and, in addition, convex). The cycle in red (around the “outside” of the graph) is chordless, but not geodesic.
This graph has seven cycles (one is Hamiltonian). Four are chordless and three of those are also geodesic (and, in addition, convex). The cycle in red (around the “outside” of the graph) is chordless, but not geodesic.

Figure 2:

Patricia’s 1990 network. Visualization created using the network R package (Butts, 2008, 2015).
Patricia’s 1990 network. Visualization created using the network R package (Butts, 2008, 2015).

Figure 3:

Patricia’s 1992 network. Nodes marked with a star are marked as “Christian Alters” in Patricia’s original diagram, and nodes colored yellow are included inside the “Sphere of the Blue Flame” in Patricia’s original diagram. Visualization created with Pajek (Batagelj and Mrvar, 2004; Mrvar and Batagelj. 2016).
Patricia’s 1992 network. Nodes marked with a star are marked as “Christian Alters” in Patricia’s original diagram, and nodes colored yellow are included inside the “Sphere of the Blue Flame” in Patricia’s original diagram. Visualization created with Pajek (Batagelj and Mrvar, 2004; Mrvar and Batagelj. 2016).

Figure 4:

Patricia’s 1993 network. Nodes marked with a star are from the box labelled “(Behind)” Patricia’s original diagram, and nodes colored yellow are included inside the “Sphere of the Blue Flame in Patricia’s original diagram. Visualization created with Paiek (Batagelj and Mrvar, 2004; Mrvar and Batageli, 2016)
Patricia’s 1993 network. Nodes marked with a star are from the box labelled “(Behind)” Patricia’s original diagram, and nodes colored yellow are included inside the “Sphere of the Blue Flame in Patricia’s original diagram. Visualization created with Paiek (Batagelj and Mrvar, 2004; Mrvar and Batageli, 2016)

Figure 5:

Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for Patricia’s 1990 network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 3 in Table 2.
Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for Patricia’s 1990 network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 3 in Table 2.

Figure 6:

Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for Patricia’s 1992 network n the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM Model 3 (right). ERGM model numbers refer to those in lame 3.
Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for Patricia’s 1992 network n the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM Model 3 (right). ERGM model numbers refer to those in lame 3.

Figure 7:

Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for Patricia’s 1993 network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM Model 3 (right). ERGM model numbers refer to those in Table 4.
Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for Patricia’s 1993 network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM Model 3 (right). ERGM model numbers refer to those in Table 4.

Figure 8:

Distribution of geodesic cycle sizes (bottom) for Patricia’s 1993 network. The points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 1k distribution (top) and ERGM Model 1 (bottom). ERGM model numbers refer to those in Table 4.
Distribution of geodesic cycle sizes (bottom) for Patricia’s 1993 network. The points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 1k distribution (top) and ERGM Model 1 (bottom). ERGM model numbers refer to those in Table 4.

Figure 9:

Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the Grey’s Anatomy sexual contact network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 3 in Table B2.
Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the Grey’s Anatomy sexual contact network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 3 in Table B2.

Figure 10:

Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the dolphin social network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 1 in Table B3.
Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the dolphin social network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 1 in Table B3.

Figure 11:

Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the Lazega law firm friendship network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 1 in Table B4.
Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the Lazega law firm friendship network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 1 in Table B4.

Figure 12:

Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the Zachary karate club network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.0k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 2 in Table B5.
Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the Zachary karate club network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.0k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 2 in Table B5.

Figure 13:

Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the Kapferer tailor shop network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 2 in Table B6.
Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the Kapferer tailor shop network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots the ERGM is Model 2 in Table B6.

Figure 14:

Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the high school friendship network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots tile ERGM is Model 2 in Table B7.
Largest geodesic cycle size (top), and distribution of geodesic cycle sizes (bottom) for the high school friendship network. In the top plot, the dashed red line is the value in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series or ERGM as labelled on the x-axis. In the bottom plots, the points shown as red diamonds joined by the red line are the values in the observed network, with the box plots showing the values in 100 networks simulated from the dk-series 2.5k distribution (left) and from the ERGM (right). In both ERGM plots tile ERGM is Model 2 in Table B7.

Figure A1:

Grey’s Anatomy sexual contact network. Male actors are colored blue, and female pink. Visualization created using the network R package (Butts, 2008, 2015).
Grey’s Anatomy sexual contact network. Male actors are colored blue, and female pink. Visualization created using the network R package (Butts, 2008, 2015).

Figure A2:

Dolphin social network. Visualization created using the network R package (Butts, 2008, 2015).
Dolphin social network. Visualization created using the network R package (Butts, 2008, 2015).

Figure A3:

Lazega law firm friendship network. Nodes are colored according to the office the person works at. Visualization created using the network R package (Butts, 2008, 2015).
Lazega law firm friendship network. Nodes are colored according to the office the person works at. Visualization created using the network R package (Butts, 2008, 2015).

Figure A4:

Zachary karate club network. Nodes are colored according to role (Instructor [green, Mr. Hi], Member [orange], or President [purple, John A.]). Visualization created using the network R package (Butts, 2008, 2015).
Zachary karate club network. Nodes are colored according to role (Instructor [green, Mr. Hi], Member [orange], or President [purple, John A.]). Visualization created using the network R package (Butts, 2008, 2015).

Figure A5:

Kapferer tailor shop network. Visualization created using the network R package (Butts, 2008, 2015).
Kapferer tailor shop network. Visualization created using the network R package (Butts, 2008, 2015).

Figure A6:

High school friendship network. Male students are colored blue, and female pink (there is one unknown colored gray). Visualization created using the network R package (Butts, 2008, 2015).
High school friendship network. Male students are colored blue, and female pink (there is one unknown colored gray). Visualization created using the network R package (Butts, 2008, 2015).

Figure A7:

Patricia’s 1992 network. Nodes marked with a dot are included inside the “Sphere of the Blue Flame” in Patricia’s original diagram. Coloring is according to network communities found with the Louvain algorithm (Blondel et al., 2008). It is apparent that the Sphere of the Blue Flame is largely included in. but does not correspond exactly with, a network community using this method, with Miranda, Stephanie, Bryony and Millie being part of another community according to the algorithm. In addition Naomi and Dordy are in the Sphere, but not in the corresponding community according to the Louvain algorithm. Dordy in particular would never be in the same community as the rest of the Sphere according to any network community algorithm, unless it also includes JC and the surrounding nodes, as Dordy is at a geodesic distance of six (via JC) from the nearest other member of the Sphere. The inclusion of Dordy in the Sphere appears to be due to spatial rather than network logic (according to the layout of Patricia’s original drawing). See Martin (2017) for more discussion of this point. Community detection and visualization were done with Pajek (Batagelj and Mrvar, 2004: Mrvar and Batagelj, 2016).
Patricia’s 1992 network. Nodes marked with a dot are included inside the “Sphere of the Blue Flame” in Patricia’s original diagram. Coloring is according to network communities found with the Louvain algorithm (Blondel et al., 2008). It is apparent that the Sphere of the Blue Flame is largely included in. but does not correspond exactly with, a network community using this method, with Miranda, Stephanie, Bryony and Millie being part of another community according to the algorithm. In addition Naomi and Dordy are in the Sphere, but not in the corresponding community according to the Louvain algorithm. Dordy in particular would never be in the same community as the rest of the Sphere according to any network community algorithm, unless it also includes JC and the surrounding nodes, as Dordy is at a geodesic distance of six (via JC) from the nearest other member of the Sphere. The inclusion of Dordy in the Sphere appears to be due to spatial rather than network logic (according to the layout of Patricia’s original drawing). See Martin (2017) for more discussion of this point. Community detection and visualization were done with Pajek (Batagelj and Mrvar, 2004: Mrvar and Batagelj, 2016).

ERGM models of the Lazega law firm friendship network_

EffectModel 1
Edges–5.256 (0.317)***
GWDEGREE1.290 (0.874)
GWESP0.597 (0.072)***
GWESP α 1.398 (0.030)***
Homophily GENDER0.535 (0.103)***
Homophily LAW SCHOOL0.137 (0.130)
Homophily OFFICE0.767 (0.111)***
Homophily PRACTICE0.485 (0.105)***
Homophily STATUS0.759 (0.104)***
Heterophily AGE–0.019 (0.009)*
Heterophily SENIORITY–0.019 (0.009)*
AIC1697.00
BIC1761.00

ERGM models of the Zachary karate club network_

EffectModel 1Model 2
Edges–3.830 (0.405)***–2.095 (0.491)***
GWDEGREE5.566 (3.376)0.988 (1.228)
GWESP (α = 0.5)1.102 (0.211)***0.358 (0.230)
Instructor 2.345 (0.527)***
President 2.369 (0.543)***
Faction abs. diff. 1 –0.246 (0.316)
Faction abs. diff. 2 –1.542 (0.492)**
Faction abs. diff. 3 –2.179 (0.605)***
Faction abs. diff. 4 –2.672 (0.626)***
AIC419.40346.80
BIC432.40385.80

Parameters for undirected networks_

EffectDescription
EdgesBaseline density
Degree k Nodes of degree k. A positive parameter indicates over-representation of nodes of degree k. “Degree k – l indicates nodes of degree between the values of k and l inclusive.
GWDEGREEGeometrically weighted degree distribution. A positive parameter indicates anti-preferential attachment (Hunter, 2007). See also Levy (2016).
GWDSPGeometrically weighted dyadwise shared partner.
GWESPGeometrically weighted edgewise shared partner. A positive parameter indicates transitivity (closure).
Homophily c Homophily on categorical attribute c. A positive parameter value indicates an edge preferentially forming between nodes with the same value of the categorical attribute. This may be shown instead as “a – b” for differential homophily: homophily specifically between values a and b of a categorical attribute, rather than uniform homophily on an attribute.
Heterophily c Heterophily on continuous attribute c. This is based on the absolute value of the difference of the attribute values of two nodes.
a ActivityActivity on binary attribute a. A positive parameter value indicates that nodes with the binary attribute are more likely to have an incident edge.
a Interactioninteraction on binary attribute a. A positive parameter value indicates that two nodes with the binary attribute are more likely to have an edge between them.

Summary statistics of the networks_

NetworkNComponentsMean degreeDensityClustering coefficientAssortativity coefficient
Patricia 19901412.570.197800.40000-0.25000
Patricia 19928522.210.026330.10345-0.46399
Patricia 199310752.130.020100.10266-0.37400
Grey’s Anatomy4442.090.048630.00000-0.22567
Dolphins6215.130.084080.30878-0.04359
Zachary karate club3414.590.139040.25568-0.47561
Kapferer tailor shop3918.100.213230.38506-0.18269
Law firm friendship71311.240.160560.448620.07948
High school friendship13436.060.045560.475400.28718

ERGM models of Patricia’s 1990 network_

EffectModel 1Model 2Model 3
Edges-2.023 (0.507)***-2.030 (0.503)***-2.391 (0.669)***
GWESP0.697 (0.341)*0.710 (0.355)*0.861 (0.505)
Degree 21.029 (0.573)  
Degree 2-3 1.006 (0.568) 
Degree 3  1.501 (0.584)*
AIC90.6290.6184.12
BIG98.1698.1491.65

ERGM models of Patricia’s 1992 network_

EffectModel 1Model 2Model 3
Edges-4.588 (0.311)***-6.047 (0.561)***-8.392 (0.775)***
GWDEGREE1.397 (0.503)**1.908 (0.560)***1.838 (0.572)**
GWESP0.793 (0.173)***0.764 (0.178)***0.608 (0.177)***
Activity Christian 0.734 (0.196)***0.772 (0.217)***
Homophil y Christian 0.377 (0.205)0.305 (0.215)
Activity Integrated 0.232 (0.310)0.150 (0.331)
Homophily Integrated 0.427 (0.350)0.290 (0.380)
Activity Sphere  0.646 (0.200)**
Homophily Sphere  2.744 (0.513)***
AIC854.40843.20782.60
BIC872.90886.40838.20

ERGM models, reproducing those in Hummel et al_ (2012), of the Kapferer tailor shop network_

EffectModel 1Model 2
Edges–3.082 (0.567)***–2.997 (0.523)***
GWDEGREE0.360 (0.935) 
GWDSP (o = 0.25)–0,129 (0.051)*–0.130 (0.052)*
GWESP (α = 0.25)1.491 (0.343)***1.436 (0.286)***
AIC732.70732.20
BIC751.10746.00

ERGM models of the Grey’s Anatomy sexual network_

EffectModel 1Model 2Model 3
Edges–1.442 (0.241)***–0.287 (0.564)–0.844 (0.636)
Homophily Sex–3.133 (0.718)***–3.428 (0.741)***–3.542 (0.732)***
Degree 12.026 (0.500)***3.533 (1.058)***3.393 (1.000)***
Degree 2 1.828 (0.911)*1.743 (0.858)*
Degree 3 0.988 (0.805)0.983 (0.769)
Heterophily Birth year –0.132 (0.030)***–0.142 (0.032)***
Attending – Attending 1.172 (0.508)*1.085 (0.533)*
Attending – Chief 1.137 (0.682)1.004 (0.699)
Attending – Non-Staff –0.714 (0.642)–0.834 (0.648)
Attending – Nurse 0.109 (0.988)–0.058 (1.215)
Attending – Other 0.490 (0.789)0.345 (0.874)
Attending – Resident 1.041 (0.502)*1.004 (0.502)*
Chief-Non-Staff –0.156 (1.183)–0.517 (1.316)
Chief – Resident 0.438 (1.080)0.427 (1.096)
Intern – Intern 5.003 (1.904)**4.611 (1.753)**
Non-Staff-Non-Staff –1.289 (1.312)–1.431 (1.266)
Non-Staff – Resident 0.395 (0.593)0.398 (0.604)
Nurse – Resident 1.147 (0.847)1.554 (0.861)
Homophily Black  2.326 (0.754)**
Homophily White  0.856 (0.392)*
AIC302.10278.40271.30
BIC316.70365.80368.40

ERGM models of the high school friendship network_

EffectModel 1Model 2Model 3
Edges–7.000 (0.570)***–8.542 (0.471)***–8.574 (0.457)***
GWDEGREE2.447 (0.385)***3.062 (0.266)***3.037 (0.259)***
GWDEGREE decay1.563 (0.113)***  
GWDSP (α = 0.5)–0.014 (0.031)0.049 (0.023)*0.047 (0.022)*
GWESP1.210 (0.079)***  
GWESP α 1.157 (0.029)***  
GWESP (α = 1.2) 1.344 (0.069)***1.334 (0.067)***
Homophily Class1.057 (0.086)***1.090 (0.084)***1.081 (0.080)***
Homophily Sex  0.171 (0.086)*
AIC2410.001937.001975.00
BIC2459.001972.002018.00

ERGM models of the dolphin social network_

EffectModel 1Model 2
Edges–0.821 (0.642)–1.553 (3.122)
GWDEGREE–2.148 (0.647)***–0.522 (3.260)
GWDSP (α = 0.7)–0.305 (0.067)*** 
GWESP (α = 0.1)0.984 (0.151)*** 
GWDSP –0.250 (0.368)
GWDSP α  0.834 (0.669)
GWESP 0.630 (0.421)
GWESP α  1.082 (0.324)***
AIC1014.001014.00
BIC1036.001047.00

ERGM models of Patricia’s 1993 network_

EffectModel 1Model 2Model 3Model 4
Edges-4.941 (0.282)***-6.609 (0.470)***-9.914 (0.869)***-10.169 (0.901)***
GWDEGREE1.501 (0.443)***2.384 (0.547)***2.314 (0.550)***2.249 (0.538)***
GWESP0.870 (0.163)***0.835 (0.168)***0.656 (0.169)***0.643 (0.172)***
Activity Christian 0.708 (0.190)***0.747 (0.203)***0.789 (0.203)***
Activity Integrated 0.540 (0.243)*0.507 (0.258)*0.580 (0.247)*
Homophily Christian 0.473 (0.203)*0.453 (0.205)*0.512 (0.214)*
Homophily Integrated 0.725 (0.252)**0.670 (0.260)**0.828 (0.271)**
Activity Sphere  0.660 (0.192)***0.729 (0.194)***
Homophily Sphere  3.611 (0.730)***3.600 (0.744)***
Activity Behind   0.631 (0.377)
AIC1094.001062.00975,60975.00
BIC1114.001108.001035.001041.00
DOI: https://doi.org/10.21307/joss-2020-002 | Journal eISSN: 1529-1227 | Journal ISSN: 2300-0422
Journal RSS Feed
Language: English
Page range: 35 - 76
Published on: Oct 1, 2020
Published by: International Network for Social Network Analysis (INSNA)
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Geodesic cycle,
Exponential random graph model,
ERGM,
-series random graphs,
Social networks,
Fictional networks,
Dissociative identity disorder
Related subjects:
Social sciences,
Social sciences, other

© 2020 Alex Stivala, published by International Network for Social Network Analysis (INSNA)
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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