Non-backtracking walk centrality for directed networks
Non-backtracking walk centrality for directed networks
复制标题
有向网络的非回溯游走中心性
DOI：
10.1093/comnet/cnx025
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
V. Noferini
中科院分区：
文献类型：
--
作者：
F. Arrigo;P. Grindrod;D. Higham;V. Noferini
zeta函数理论为生成函数提供了一个表达式，
nominations of
有向网络上的非回溯行走计数。我们展示了
表达式可用于
产生一个中心性度量，消除回溯行走，
不花钱。我们还表明，
生成函数的收敛半径由SPECT确定
三乘三的朗姆酒
分块矩阵涉及原邻接矩阵。这给
这是一种选择合适的方法
衰减参数的值。我们发现三个重要的a
当我们
使用这种技术来消除网络中的遍历，
不太可能有关联
首先，我们获得了更大范围的选择衰减帕拉
米第二，由于半径
母函数的收敛性是不变的，
在所有特定类型的节点中，
我们可以通过减少t的维数来提高计算效率，
结果本征值
问题.第三，定义中心的线性系统的维数
ty措施可能会减少
以同样的方式。我们证明了新的中心性测度可能是interp
称为标准Katz
在一个修改过的网络上，其中添加了自循环，并且其中
l边是增广的
负权重。我们还给出了多层解释，
有负权游动
层间补偿唯一非emp上的回溯行走
ty层。学习极限
当衰减参数接近其上限时，
提出一种基于特征向量的
在这个有向网络设置中的非回溯中心性度量。
我们发现两乘两
在以往的研究中出现的块矩阵集中在无向网络
必须扩展到新的
三乘三块结构，以允许有向边缘。我们阐明
e上的中心性度量
一个合成网络，其中它被证明可以消除本地化效应p
在标准Katz中重新发送
中心性最后，我们给出了真实的网络的结果。
The theory of zeta functions provides an expression for the generating fu
nction of
nonbacktracking walk counts on a directed network. We show how this
expression can be used to
produce a centrality measure that eliminates backtracking walks at
no cost. We also show that the
radius of convergence of the generating function is determined by the spect
rum of a three-by-three
block matrix involving the original adjacency matrix. This giv
es a means to choose appropriate
values of the attenuation parameter. We find that three important a
dditional benefits arise when we
use this technique to eliminate traversals around the network that
are unlikely to be of relevance.
First, we obtain a larger range of choices for the attenuation para
meter. Second, because the radius
of convergence of the generating function is invariant under the remov
al of certain types of nodes,
we can gain computational efficiencies through reducing the dimension of t
he resulting eigenvalue
problem. Third, the dimension of the linear system defining the centrali
ty measures may be reduced
in the same manner. We show that the new centrality measure may be interp
reted as standard Katz
on a modified network, where self loops are added, and where nonreciproca
l edges are augmented
with negative weights. We also give a multilayer interpretation, wh
ere negatively weighted walks
between layers compensate for backtracking walks on the only non-emp
ty layer. Studying the limit
as the attenuation parameter approaches its upper bound allows us
to propose an eigenvector-based
nonbacktracking centrality measure in this directed network setting.
We find that the two-by-two
block matrix arising in previous studies focused on undirected networks
must be extended to a new
three-by-three block structure to allow for directed edges. We illustrat
e the centrality measure on
a synthetic network, where it is shown to eliminate a localization effect p
resent in standard Katz
centrality. Finally, we give results for real networks.