Dynamics On and Of Complex Networks, Volume 2 by Animesh Mukherjee Monojit Choudhury Fernando Peruani Niloy Ganguly & Bivas Mitra

Author:Animesh Mukherjee, Monojit Choudhury, Fernando Peruani, Niloy Ganguly & Bivas Mitra
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

where C i t is the cluster membership for at time t and A ij t represents the group interaction. The group interaction is computed by A ij t  = (C i t ) T R ij t C j t  . Therefore, for each temporal m-mode graph at time t, its snapshot cost can be formulated as

and its history cost is expressed as

where w a ij is an importance factor for every pair of modes i and j, and w b i is a relative importance factor for each mode i.

3.5 Matching Metrics

A matching metric is a similarity function, which measures how similar two communities are. It is often used in two-stage approaches (see Sect. 4.1) to connect similar communities. One can measure the similarity between two temporal clusters at different time steps and naturally obtain how one community evolves from one time step to the following time steps.

Hopcroft et al. [44] defined a match function. Let C and C′ be two clusters; their match value is written as follows:

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