  Taking a pragmatic approach to the processes involved in the phenomena of
collective opinion formation, we investigate two specific modifications to the
co-evolving network voter model of opinion formation, studied by Holme and
Newman [1]. First, we replace the rewiring probability parameter by a
distribution of probability of accepting or rejecting opinions between
individuals, accounting for the asymmetric influences in relationships among
individuals in a social group. Second, we modify the rewiring step by a
path-length-based preference for rewiring that reinforces local clustering. We
have investigated the influences of these modifications on the outcomes of the
simulations of this model. We found that varying the shape of the distribution
of probability of accepting or rejecting opinions can lead to the emergence of
two qualitatively distinct final states, one having several isolated connected
components each in internal consensus leading to the existence of diverse set
of opinions and the other having one single dominant connected component with
each node within it having the same opinion. Furthermore, and more importantly,
we found that the initial clustering in network can also induce similar
transitions. Our investigation also brings forward that these transitions are
governed by a weak and complex dependence on system size. We found that the
networks in the final states of the model have rich structural properties
including the small world property for some parameter regimes. [1] P. Holme and
M. Newman, Phys. Rev. E 74, 056108 (2006).
