Note: GraphSpace is moving into GeomStats python package! We apologize for possible usability issues within the transition process. Please check geomstats for an updated version!

GraphSpace

Graph Space Package

This python package allows to study populations of networks in the Graph Space geometric setting [1], as a special case of Structure Space introduced in [2]. The package is organized as follow:

core:

• Graph: class creating a graph object
• GraphSet: class creating a graph set
• Mean: class computing the Frechèt Mean and the variance of a set of graphs [2]
• MeanIterative: bootstrapped version of Frechèt Mean [2]

distance:

• euclidean: compute the euclidean distance between nodes and vector attributes

matcher:

• Matcher: parent class created to match two graphs
• child classes: whatever algorithm used to match two different networks, based on topology, node attributes and edge attributes. Child class gives back a reordered node sequence optimizing the matching criteria ID: identity match GA: graduate assignment match[2] GAS, GAS1: solving directly the optimization problem (GAS1 tackles the linearized version)
• alignment: class aligning two graphs with a specified matcher

AlignCompute:

• mean_aac: compute the Frechet Mean with the AAC algorithm and a given matcher [1]
• gpca_aac: compute the Geodesic Principal Components with AAC and a given matcher [1]
• ggr_aac: compute the Generalized Geodesic Regression with AAC and a given matcher [4]

Acknowledgement: A great acknowledgment goes to Brijnesh Jain, whose code is used as a starting point for this package. Gianluca Zeni has been massively contributing on the implementation of the python package.

[1] Calissano, Anna, Feragen, Aasa and Vantini, Simone "Graph Space: Geodesic Principal Components for aPopulation of Network-valued Data" MOX Report (2020)

[2] Jain, Brijnesh J., and Klaus Obermayer. "Structure spaces." Journal of Machine Learning Research 10.Nov (2009): 2667-2714.

[3] Gold, Steven, and Anand Rangarajan. "A graduated assignment algorithm for graph matching." IEEE Transactions on pattern analysis and machine intelligence 18.4 (1996): 377-388.

[4] Calissano, Anna, Feragen, Aasa, and Vantini, Simone "Graph-on-scalar Regression: Modelling Equivalence Classes of Networks from Scalars" In preparation (2020)