Scaling of average weighted shortest path and average receiving time on weighted hierarchical networks

The entire mean weighted first-passage time on a family of weighted treelike networks

“…For any weighted treelike networks, the weighted shortest path λ ij of G n is equal to the effective resistance r ij between node i and j , i.e, r ij = λ ij . By definition the average weighted shortest path λ n of the graph G n is given by 4 …”

“…Especially, weighted networks 1 2 represent the natural framework to describe natural, social, and technological systems 3 . The deterministic weighted networks have attracted increasing attentions because many network characteristics are exactly solved through their quantities, such as mean weighted first-passage time, average weighted shortest path 4 etc.…”

“…Sun et al . 4 discussed a family of weighted hierarchical networks which are recursively defined from an initial uncompleted graph. Zhu et al .…”

MFPT calculation for random walks in inhomogeneous networks

“…With both cognitive and social components, PSO has been known to converge to a reasonably good solution very quickly [47,45]. As there are many networks where the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale [48,49], the quick optimization process of PSO is useful when networks change in real time. HPSO was used in order to eliminate particles from stagnating at suboptimal solutions [45].…”

Asymptotic formula on average path length of fractal networks modeled on Sierpinski gasket

“…There are also some complex networks modelled on self-similar fractals, for example, Liu and Kong [12] and Chen et al [4] study Koch networks, Zhang et al [17] investigate the networks constructed from Vicsek fractals. See also Dai and Liu [5], Sun et al [15] and Zhou et al [20].…”