TY - JOUR
T1 - Configuring random graph models with fixed degree sequences
AU - Fosdick, Bailey K.
AU - Larremore, Daniel B.
AU - Nishimura, Joel
AU - Ugander, Johan
N1 - Funding Information:
\ast Received by the editors August 1, 2016; accepted for publication (in revised form) April 20, 2017; published electronically May 8, 2018. All authors contributed equally to this work. http://www.siam.org/journals/sirev/60-2/M108717.html Funding: This work was funded by the American Mathematical Society, the Santa Fe Institute Omidyar Fellowship, a David Morgenthaler II Faculty Fellowship, and the National Science Foundation under grant SES-1461495. \dagger Department of Statistics, Colorado State University, Ft. Collins, CO 80523 (bailey.fosdick@ colostate.edu). \ddagger Santa Fe Institute, Sante Fe, NM 87501 (larremore@santafe.edu). \S School of Mathematical and Natural Sciences, Arizona State University, Glendale, AZ 85306 (joel.nishimura@asu.edu). \P Management Science \& Engineering, Stanford University, Stanford, CA 94305 (jugander@ stanford.edu).
Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.
PY - 2018
Y1 - 2018
N2 - Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal networks. The most popular random graph null models, called configuration models, are defined as uniform distributions over a space of graphs with a fixed degree sequence. Commonly, properties of an empirical network are compared to properties of an ensemble of graphs from a configuration model in order to quantify whether empirical network properties are meaningful or whether they are instead a common consequence of the particular degree sequence. In this work we study the subtle but important decisions underlying the specification of a configuration model, and we investigate the role these choices play in graph sampling procedures and a suite of applications. We place particular emphasis on the importance of specifying the appropriate graph labeling-stub-labeled or vertex-labeled-under which to consider a null model, a choice that closely connects the study of random graphs to the study of random contingency tables. We show that the choice of graph labeling is inconsequential for studies of simple graphs, but can have a significant impact on analyses of multigraphs or graphs with self-loops. The importance of these choices is demonstrated through a series of three in-depth vignettes, analyzing three different network datasets under many different configuration models and observing substantial differences in study conclusions under different models. We argue that in each case, only one of the possible configuration models is appropriate. While our work focuses on undirected static networks, it aims to guide the study of directed networks, dynamic networks, and all other network contexts that are suitably studied through the lens of random graph null models.
AB - Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal networks. The most popular random graph null models, called configuration models, are defined as uniform distributions over a space of graphs with a fixed degree sequence. Commonly, properties of an empirical network are compared to properties of an ensemble of graphs from a configuration model in order to quantify whether empirical network properties are meaningful or whether they are instead a common consequence of the particular degree sequence. In this work we study the subtle but important decisions underlying the specification of a configuration model, and we investigate the role these choices play in graph sampling procedures and a suite of applications. We place particular emphasis on the importance of specifying the appropriate graph labeling-stub-labeled or vertex-labeled-under which to consider a null model, a choice that closely connects the study of random graphs to the study of random contingency tables. We show that the choice of graph labeling is inconsequential for studies of simple graphs, but can have a significant impact on analyses of multigraphs or graphs with self-loops. The importance of these choices is demonstrated through a series of three in-depth vignettes, analyzing three different network datasets under many different configuration models and observing substantial differences in study conclusions under different models. We argue that in each case, only one of the possible configuration models is appropriate. While our work focuses on undirected static networks, it aims to guide the study of directed networks, dynamic networks, and all other network contexts that are suitably studied through the lens of random graph null models.
KW - Complex networks
KW - Configuration model
KW - Graph enumeration
KW - Graph sampling
KW - Markov chain monte carlo
KW - Permutation tests
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U2 - 10.1137/16M1087175
DO - 10.1137/16M1087175
M3 - Review article
AN - SCOPUS:85046685956
SN - 0036-1445
VL - 60
SP - 315
EP - 355
JO - SIAM Review
JF - SIAM Review
IS - 2
ER -