Algorithm 1: Robustness optimization method for communication in hypernetworks
Step	Description
input	Initial Hypernetwork $H_0$, Total hyperedge number M, Proportion of newly added hyperedges q, Communication Robustness Optimization Method Method
output	Communication Efficiency of $H_0$, $BIP\_T$
Initialization	generating hypernetwork $H_0$ with M hyperedges
1	do Calculate for each node in $H_0$, its hyper-betweenness, distance entropy, characteristic subgraph centrality, and Fiedler-value-based centrality, and, for each of these centrality measures, identify the corresponding set of peripheral nodes $V_{\mathrm{margin}\_\mathrm{HBC}}$, $V_{\mathrm{margin}\_\mathrm{HDI}}$, $V_{\mathrm{margin}\_\mathrm{HC}\_\mathrm{sub}}$, and $V_{\mathrm{margin}\_\mathrm{HC}\_\mathrm{Fiedler}}$.
2	if $H_0$ is k-uniform hypernetwork:
3	do add_node = k
4	else: do Calculate the average number m of nodes contained in the hyperedges of the hypernetwork;
5	do add_node = m
6	switch(Method) {
7	case HBC:
8	do from the peripheral node set $V_{\mathrm{margin}\_\mathrm{HBC}}$, select add_node nodes to form a new hyperedge, and repeat this edge-addition process until the prescribed edge-addition ratio is reached;
9	break;
10	case HDI:
11	do from the peripheral node set $V_{\mathrm{margin}\_\mathrm{HDI}}$, select add_node nodes to form a new hyperedge, and repeat this edge-addition process until the prescribed edge-addition ratio is reached;
12	break;
13	case HC_sub:
14	do from the peripheral node set $V_{\mathrm{margin}\_\mathrm{HC}\_\mathrm{sub}}$, select add_node nodes to form a new hyperedge, and repeat this edge-addition process until the prescribed edge-addition ratio is reached;
15	break;
16	case HC_Fiedler:
17	do from the peripheral node set $V_{\mathrm{margin}\_\mathrm{HC}\_\mathrm{Fiedler}}$, select add_node nodes to form a new hyperedge, and repeat this edge-addition process until the prescribed edge-addition ratio is reached;
18	break;}
19	do Denote the hypernetwork with the newly added hyperedges as $H_q$;
20	do Independently attack the hypernetworks $H_0$ and $H_q$, and compute the communication efficiency CE of both hypernetworks.
21	do Calculate $BIP\_T$