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 .