Topological Structure of Manufacturing Industry Supply Chain Networks
Table 6
Node-level metrics used and their SCN implications.
Mathematical representation
SCN implication
Degree ()
In undirected networks, the degree of node is given as
In directed networks, the degree of node is separated into in- and out-degrees, as follows:
where is any element of the adjacency matrix .
Represents the number of direct neighbours (connections) a given firm has. For instance, in a given SCN, the firm with the highest degree (such as the integrators that assemble components) is deemed to have the largest impact on operational decisions and strategic behaviours of other firms in that particular SCN. Such a firm has the power to reconcile the differences between various other firms in the SCN and align their efforts with greater SCN goals [23]. In directed networks, the firms which have high in-degree are considered to be “integrators” who collect information from various other firms to create high-value products. In contrast, the firms which have high out-degree are considered to be “allocators” who are generally responsible for distribution of high-demand resources to other firms and/or customers.
The betweenness centrality of a node is defined as
where and are nodes in the network, which are different from , denotes the number of shortest paths from to , and is the number of shortest paths from to that lies on.
Betweenness centrality of a firm is the number of shortest path relationships going through it, considering the shortest path relationships that connect any two given firms in the SCN. Therefore, it indicates the extent to which a firm can intervene over interactions among other firms in the SCN by being a gatekeeper for relationships [23]. Those firms with high levels of betweenness generally play a vital role in SCNs—mainly owing to their ability to increase the overall efficiency of the SCN by smoothing various exchange processes between firms.
where is the length of the shortest path between two nodes and (note that for unweighted graphs with no geodesic distance information, each link is assumed to be one unit of distance). The closeness centrality of each node is a number between 0 and 1.
Closeness centrality is a measure of the time that it takes to spread the information from a particular firm to the other firms in the network. While it is closely related to betweenness centrality, closeness is more relevant in situations where a firm acts as a generator of information rather than a mere mediator/gatekeeper. Firms with high closeness centrality levels enable the overall SCN to be more market sensitive (i.e., responsive) by spreading the actual market demand information with the other upstream firms [9].
