Here, we present six MSTs of 82 stocks in KSE-100 of Pakistan stock market before and after three general elections (2018, 2013, and 2008). The stocks (nodes) are colored based on their business sectors, as per Table 2.
Figure 1 shows the MST map before the general election of 2018. There is no single most dominant stock, but four principal nodesFootnote 1: Nishat Mills (NML 6), D.G. Khan Cement (DGKC 5), Kohat Cement (KOHC 5), and Sui Northern Gas (SNGP 5). Therefore, MST highlights the strong dependency of Pakistan’s economy on cement, textile, and oil and gas sectors before the 2018 election. Additionally, the results show that the stocks in the cement (red) and oil and gas (yellow) sectors form clusters and connect with each other. However, companies in the commercial banks sector (blue) are split into two groups, one at the bottom left of the map and one on the middle-right side. Furthermore, a strong intermediary role is being played by SNGP, which is carrying the highest betweenness centrality score of 2265.
The MST map after election 2018 of the KSE-100 index companies is presented in Fig. 2. We observe the scattered pattern of the commercial banking sector, where banks are linked to companies from other sectors. Similarly, oil and gas companies are separated from one major cluster before elections 2018 to a disbursed distribution after elections period. The split of these two sectors possibly reflect different responses to the risks constituted by general elections. In terms of connectivity, a main hub node is Lucky Cement (LUCK 10), followed by three key nodes: D.G. Khan Cement (DGKC 7), ENGRO Corporation (ENGRO 5), and Kohat Cement (KOHC 5). Several emerging countries such as South Africa (Majapa and Gossel 2016), Brazil (Tabak et al. 2010), China (Zhuang et al. 2008), and India (Sinha and Pan 2007) have key nodes in the MST, which is not uncommon on Pakistan’s stock market. In sum, the MST shows a star-like structure after the general elections of 2018, possibly reflecting a structural transition.
Figure 3 represents the 2013 pre-election MST map of the KSE-100 network. The figure shows a tree-like structure of the MST (Nobi et al. 2015) due to low value of centrality. The three key nodes of Mapple Leaf Cement (MLCF), Pak Suzuki Motors (PSMC), and Searle Company (SEARL) have a maximum of five connections each in the 2013 pre-election period. In addition, there is no major cluster formation and reduced connectivity in the network. Only three cement sector companies—DGKC, MLCF, and PIOC—connect with each other, the rest linking with companies from different sectors. Further, companies from almost all the sectors are scattered, and around 77% of nodes have two or fewer connections.
The MST map of the KSE-100 index after the general elections of 2013 is presented in Fig. 4. We can observe a slight increase in the degree of connectivity per node for Maple Leaf Cement (MLCF 6), while four nodes—Cherat Packaging (CPPL), Hub Power (HUBC), Kohinoor Textile Mills (KTML), and Nishat Mills (NML)—have five connections each. Additionally, Searle (SEARL) and Pak Suzuki (PSMC) nodes have now two and one connection, respectively. This reconfiguration possibly represents the diversification of these companies after the general elections. The MST in post the 2013 election has a tree-like structure compared to the star-like structure in the post 2018 election period.
The pre-2008 election MST map of the KSE-100 index companies is presented in Fig. 5. A major node is Pakistan Petroleum (PPL 9), followed by two significant nodes—Nishat Mills (NML 7) and Muslim Commercial Bank (MCB 5). Hence, PPL is the dominating company in the network before the 2008 general elections, and companies surrounding this node will be directly influenced by any shock due to the general elections (Sharif et al. 2016). Additionally, the oil and gas sector (yellow) and commercial banking sector (blue) cluster, whereas cement sector nodes (FCCL, MLCF, CHCC, PIOC, ACPL, LUCK) are spread over the entire network.
Figure 6 shows the post 2008 election MST map of KSE-100 index network. We observe a tree-like structure and reduction in the degree of connections per node compared to the star-like structure before the election. D.G. Khan Cement (DGKC 7) is the most significant and central node, followed by Attock Refinery (ATRL 6) and Oil and Gas Development Company (OGDC 5). However, PPL has moved from nine connections before election to three. Additionally, companies from the cement sector form a cluster. Overall, the results show a structural change in the network topology from before to after the 2008 general elections.
Sectorial centrality measures
We here present the sectorial centrality properties of the KSE-100 index MST network for all three general elections. As centrality measures are important in network analysis to examine the behavior of networks (Ghanbari et al. 2018), we present the average sectorial degree of centrality in Fig. 7. The figure shows the cement sector nodes have a mean of approximately three incident edges, followed closely by oil and gas and fertilizer sectors with means of two and half. We can observe a large increase in the average number of incident edges for the nodes in the cement sector after the 2018 general elections compared to any other sectors. The other sector that exhibits an increase in connectivity is the paper and board sector after the 2013 elections. This increase in the number of edges highlights an expansion in the economic activities of these sectors in the elections periods. Additionally, the results show a consistent decrease in the connectivity of commercial banks in all the three post-election periods, compared to the high average degree of connections during the pre-elections periods. The comparison between pre- and post-elections centrality metrics shows a consistent average connectivity in the textile sector during all periods, except for a substantial increase in the post 2013 election period.
Figure 8 presents the average sectorial closeness centrality for the periods before and after the elections. The cement sector has a large average closeness centrality of 0.26 after the 2018 election, followed by the oil and gas (0.22), pharmaceutical (0.22), technology and communications (0.21), and paper and board 0.21 sectors over the same period. This could be interpreted as the key role of these sectors in the MST after the 2018 election. Additionally, the cement sector is closer to other sectors’ nodes as the companies from this sector have the highest average closeness centrality. By contrast, the lowest average closeness centrality is registered by the paper and board sector (0.090 after the 2008 general elections. However, the overall average closeness centrality is 0.15 for all sectors during all periods.
Regarding average sectorial betweenness centrality, Fig. 9 shows that the fertilizer sector has the maximum number of shortest routes and has a strong mediating role, especially before the 2013 elections. Additionally, the average betweenness centralities of the oil and gas and cement sectors are also high. Similarly, an increase in the mediation effect of the cement sector is also registered after the 2018 election. Furthermore, the food and personal care products, tobacco, pharmacy, and automobile sectors present the lowest overall average betweenness centrality scores, reflecting their weak mediation effects.