Network analysis was used to study the structure and time evolution of driven
three-dimensional complex plasma clusters. The clusters were created by suspending
micron-size particles in a glass box placed on top of the rf electrode in
a capacitively coupled discharge. The particles were highly charged and manipulated
by an external electric �eld that had a constant magnitude and rotated
uniformly in the horizontal plane. Depending on the frequency of the applied electric
�eld, the clusters rotated in the direction of the electric �eld or remained stationary.
The three-dimensional positions of all particles were measured using stereoscopic
digital in-line holography.
The network approach was used to elucidate the structural changes in the cluster
consisting only of a very limited number of particles (64). The Analysis revealed an
interplay between two competing symmetries in the cluster. Spherical and cylindrical
ordering of the particles was examined by comparing network measures of the
experimental data with null models. The null models were arti�cial data with a certain
number of points in perfectly spherical order, and the rest in cylindrical order.
The well established network measures local connectivity, clustering coe�cient and
average path length were considered. Network analysis of the clusters showed
that the rotating cluster was more cylindrical than the nonrotating cluster.
These �ndings were in agreement with the estimate of the radial con�nement
with the aid of a dynamical force balance. Neglecting friction and inertial forces due
to the low particle velocities in the cluster, the pro�le of the electrical con�nement
could be estimated by calculating the repulsing Yukawa-type interaction between
the particles. The radial con�nement was shown to be stronger in the case of cluster
rotation, increasing the cylindricity of the cluster.
The emergence of vertical strings of particles was also con�rmed by using a network
analysis. While the traditional method of a �xed threshold has limitations such
as erroneously including passing by particles and a somewhat arbitrary threshold,
community �nding algorithms yield a more elegant approach of �nding structures
in complex systems. With the aid of multislice networks, it is possible to examine
the whole time series at once and thus resolve the time evolution of the strings.
As we demonstrated, network analysis is a powerful tool to analyze the structure
of complex plasma clusters and may have numerous applications in other complex
systems where the characertization of the spatial structure plays a vital role.
