复杂网络理论分析：定向加权事故原因网络（DWACN）建模与研究

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"定向加权事故原因网络（DWACN）的建模和分析方法" 在当前的研究论文中，作者提出了一个创新的模型——定向加权事故原因网络（DWACN），该模型利用复杂网络理论来深入理解复杂系统中事故的发生原因。 DWACN是一种特殊类型的网络，它能够反映事故因果关系的复杂性和动态性。文章的主要亮点包括建立DWACN的方法、对事故分析的深入探索以及揭示DWACN的网络特性。首先，DWACN的建模方法是研究的核心。这种方法允许研究人员构建一个有向且加权的网络，其中节点代表可能导致事故的因素，边则表示这些因素之间的因果关系，权重则表示了因果影响的程度。通过这种方式，DWACN可以捕捉到事故发生的多层次和多因素特征，从而更全面地分析事故的发生机制。其次，论文强调了对DWACN的统计属性分析。通过这种方法，研究人员可以发现DWACN具有小世界网络和无标度网络的特性。小世界网络意味着尽管网络中的节点平均距离较短，但节点之间存在紧密的联系，这反映了事故原因之间可能存在局部聚集和全局快速传播的特点。无标度网络特性则意味着网络中节点的度分布遵循幂律，即少数节点拥有大量连接，而大多数节点只有少量连接，这可能对应于某些事故原因起主导作用，而其他原因的影响较小的情况。此外，论文还提到了事件链的概念。事件链是指事故发展过程中的一系列因果事件，它们按照特定的顺序发生，最终导致事故。在DWACN中，事件链可以被识别并分析，从而帮助识别事故发生的潜在路径和关键节点，这对于预防和控制事故至关重要。这篇研究论文提供了一种新的视角来理解和分析事故原因，通过构建DWACN模型，可以更深入地挖掘事故背后的复杂因果关系，有助于提升安全管理和风险防控的效率。这种理论和方法的应用不仅限于交通领域，还可以推广到其他复杂系统的事故分析，如工业生产、环境保护和公共安全等领域。通过深入研究和应用DWACN，可以为事故预防和应急响应提供更科学的决策支持。

J. Zhou et al. / Physica A 437 (2015) 263–277 265

ships among nodes than other three kinds of networks. Thus this paper attempts to propose a method to establish directed

weighted accident causation network (DWACN). To better explore the features of DWACN, the rest of this section will intro-

duce basic statistical properties of directed weighted complex network. These properties are used by us to analyze DWACN.

A directed weighted network G with N nodes can be represented mathematically by an N × N adjacency matrix A with

elements [20].



• w

if node i points to node j,

0 otherwise

(1)

where a

takes the value 1 if node i points to node j and 0 otherwise. And w

specifies the weight on the edge if nodes i

points to node j (w

= 0 otherwise).

(1) Degree and degree distribution.

The degree of k

of a node i is the number of edges incident with the node. In directed networks, the degree of the node has

two components: the number of outgoing links: k

out



(referred to as the out-degree of the node), and the number of

incoming links: k



(referred to as the in-degree of the node). The total degree is then defined as k

= k

out

+ k

[21].

The degree distribution completely determines the statistical properties of the network, and can be characterized by

P(k) [21]. Here, P(k) means the probability of a randomly selected node whose degree is k.

(2) Node strength and node strength distribution.

Degree has generally been extended to the sum of weights when analyzing weighted networks [22], and labeled node

strength. A very significative measure of the network properties in terms of the actual weights is obtained by looking at the

vertex strength as follows [23]: in a weighted network, the number of outgoing weight of node i : s

out



, and the

number of incoming weight of node i : s



. The total weight is then defined as s

= s

out

+ s

The node strength distribution is similarities with the degree distribution, here denoted as P(s). P(s) means the

probability of a randomly selected node whose degree is s.

(3) Shortest path length, average path length and diameter.

The shortest path length is the least number of edges that connects two nodes together [22]. In our network, the weights

of edges are very similar with ties strength [23]. The weights need to be reversed before directly applying Dijkstra’s algorithm

to identify the shortest paths in these networks. Newman’s [24] and Brandes’ [25] implementation of Dijkstra’s algorithm

can be formally defined as:

= min



+ · · · +



. (2)

A measure of the typical separation between two nodes in the graph is given by the average shortest path length, defined

as the mean of geodesic length over all nodes [21]:

L =

N(N − 1)



i,j∈N, i=j

(3)

where d

is the length of the geodesic from node i to node j.

Diameter is defined as the longest of all the calculated shortest paths in a network [12].

(4) Weighted clustering coefficient.

In weighted networks, the weighted clustering coefficient is represented as c

, and the direction of edges should not be

considered. Thus for node i connecting to node j, the weight of edge is w

′

= w

+ w

); and a

′

= 1 (if a

= 1 or a

= 1).

In this way, the directed network turns into an undirected one. The weighted clustering coefficient is defined as [23]:

− 1)



j,h

′

+ w

′

)

′

. (4)

In this way we are considering not just the number of closed triplets in the neighborhood of a vertex but also their total

relative weight with respect to the strength of the vertex.

(5) Betweenness centrality.

The communication of two non-adjacent nodes, say j and h, depends on the nodes belonging to the paths connecting j

and h. Consequently, a measure of the relevance of a given node can be obtained by counting the number of geodesics going

through it, and defining the so-called node betweenness centrality. The betweenness centrality b

of a node i is defined

as [21]:



j,h∈N,j=h

jh(i)

(5)

where n

is the number of shortest paths connecting node j and node h, while n

jh(i)

is the number of shortest paths connecting

node j and node h and passing through node i.

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