Figure.2 Flowchart of oasis transition network construction
3.1.1 Oasis transition
analysis
In oasis transition network, the degree value of one oasis type node
refers to its edge number. The higher the degree value, the more
connections the node has with other nodes (Li & Xiao, 2017). The
direction and intensity of the node interactions are important
indicators in a directional and weighted network. The weighted in-degree
and out-degree are defined based on the direction and weight from the
edges. Here, in-degree and out-degree represent the transfer-in and
transfer-out areas of oasis types, respectively. Weight refers to the
converted areas between two land types. The ratio of weighted out-degree
to weighted in-degree (named ratio) is employed to determine whether a
land type is a transfer-in or transfer-out type. If the ratio greater
than 1, the land type is defined as a transfer-out type; otherwise, it
is a transfer-in type. In-degree and out-degree can be calculated as:
where is adjacency matrix of the network. If there are any connections
between th node and th node, ; else, , here , N, n represent the
number of nodes in a network, and when , . is the transition matrix. is
the element in , if represent the weighted out-degree from th node to th
node, else represent the weighted in-degree from th node to th node. The
number of , when equal to the out-degree of th node else equal to the
in-degree of th node.
3.1.2 Identification of key land
type
In the complex network, betweenness centrality is used to identify the
key node in oasis transition network, which refers to the ratio of the
shortest paths that pass through this node to all the shortest paths in
the network. The shortest path refers to the node sequence with shortest
weighted sum between two nodes, and its length is considered as the
smallest weighted sum between two nodes (Lambiotte et al. , 2019;
Sporns, 2018). In the oasis transition network, a land type with higher
betweenness centrality would have more control over the whole network,
because of more information passing through that node. The key land type
plays a vital role in affecting the interactions of land types and the
oasis transition network vitality. Betweenness centrality can be
calculated as:
where is the th node betweenness centrality, is the number of shortest
path passing the th node, and is the number of shortest path in whole
network.
3.1.3 Oasis structural
stability
Oasis type transition possibility demonstrates the oasis structural
stability in the complex network and the path length usually represents
the transition possibility of two types. Average path length are
employed to express the possibility of two types in this study (Zhanget al. , 2019). Here, the path length refers to the number of
edges in a sequence that connects two nodes in a network, and the
corresponding sequence with the shortest length between two nodes is
called the shortest path. The average length of the shortest path in a
network is the average path length. The shorter average path length, the
higher transfer efficiency is among the oasis types but a more unstable
oasis structure. The average path length was calculated as:
where is the average path length in the network. refers to the number of
nodes in the network. represents the length of the shortest path between
node and .
3.2 Driving forces for Oasis
transition
Oasis transition driving forces were explored from natural and human
aspects. Pearson’s correlation coefficient (r ) is used to express
the linear correlation between two variables (Cui et al. , 2023).
In this study, we quantified the driving forces between driving factors
and oasis changes using r -value. r -value can be expressed
as:
where and represent oasis type and the area at the th year. is the
number of samples; and represent the mean value vectors of and ,
respectively. is the correlation coefficient between and .