In this study, we explored different topological organizations of FN and SN in RC patients and HC. The findings pointed RC patients displayed altered small-worldness property and global topological organization compared with HC. Moreover, there were regions with significant abnormal being mainly distributed in frontal region, subcortical regions and central region in RC patients. In addition, RC patients showed vulnerable network resilience in both networks, and FN would be more stable than SN across participants.
4.1 Network Properties
Although the global and regional brain network properties in breast cancer and lung cancer patients are reported in neuroimaging research using fMRI [32, 33] and DTI , rectal carcinoma is still little. Compared with HC, the functional networks of RC patients displayed a higher shortest path length (λ) and decreased small-worldness( ), reflecting reduced global integration and disrupted organization balance [2, 17]. Our results also revealed increased local efficiency in RC patients. It is a measure of local information transmission among adjacent nodes and therefore an indication of network segregation . Previous studies demonstrated reduced local efficiency, a common measure of the brain network's response to computational attack, associated with breast cancer patients [17, 35]. Due to brain structural damage, decreased local efficiency would affect the fault tolerant ability of brain network. More detail, the result of weakening network fault tolerance is that if a node in the brain is damaged, the connection between previously linked nodes would be greatly affected . Therefore, reduced local efficiency is a risk factor for RC patients. Recently, researchers use graph theory to analyze complex brain functional networks after chemotherapy. It has been proved that chemotherapy-related cognitive deficits were associated with abnormal topological alterations of brain functional and structural network [37-39]. In this study, increased shortest path length and decreased local efficiency in RC patients with surgery and chemotherapy could be seen as a brain compensation mechanism, which included changing the global pathway and adjusting regional activity to preserve a seesaw-like balance of the brain network.
RC patients showed increased clustering coefficients (γ), small-worldness( ) and global efficiency in SN (Figure 2). Abnormal small-worldness property of SN indicated that the local specialization and global integration of brain in RC patients were disrupted, where the SN tended to be more randomized. Global efficiency is the inverse of the average shortest path between nodes. When nodes could interact directly, the efficiency is high . Therefore, global efficiency is an indicator of network function integration and parallel information processing capability . The present results of abnormal network properties reflected the undesired topological organization in SN, which exhibited that the deficits of emotional and cognitive processing in RC patients might result from network damages. Besides, the increased network properties of SN in RC patients might suggest that local nerve fibers reconstructed in response to the abnormalities in brain functional network. The compensatory response of the SN is activated for maintaining brain functional integrity to compensate the cognitive impairment caused by chemotherapy to RC patients . Aforementioned evidences illuminated that cognitive deficit related to RC patients may act via disrupted coordination between global and regional networks.
4.2 Regional nodal parameters
To explore the functional and structural characteristics of the human brain more accurately and quantitatively, our study employed a new standard brain atlas, containing 246 brain regions. This atlas would allow brain network analysis to use predefined nodes in an informed manner . Therefore, more detailed division of brain regions provide better help in multi-modal data analysis. We observed decreased only in FN of RC patients. The significantly changed regions were located in bilateral basal ganglia, bilateral thalamus, right parahippocampal gyrus, right precuneus, and right lateral occipital cortex. The basal ganglia is not only related to motor control, but also related to the cognitive and limbic functions . Moreover, basal ganglia is the collection of subcortical nuclei surrounding the thalamus . Abnormal activation of basal ganglia/thalamus was found in the depressive studies [44, 45], suggesting that abnormalities in these brain regions may lead to abnormal emotional processing mechanisms. Prior studies reported that parahippocampal gyrus and precuneus were associated with memory function, so alterations in these regions might affect memory decline [46, 47]. Task-fmri study of memory factors found that the occipital cortex of cancer patients was more significantly correlated with vigor and fatigue scores . Frequent fatigue is a common symptom of cancer patients . Aforementioned evidences indicated that the decreased of FN in this study represented alterations in regional characteristics of the brain network, which further affected the cognitive impairment of RC patients.
Furthermore, the increased nodal efficiency was mainly in frontal cortex, left amygdala, bilateral cingulate gyrus, left inferior parietal lobule, and right precentral gyrus in FN and SN for RC cancer patients. In experiments with high-demand condition, the right inferior frontal gyrus as well as other components of the two hemisphere working memory circuitry in cancer patients were found greater activation than the control group in a prior study . These abnormalities might be a compensation mechanism to preserve normal thinking and responsiveness in cancer patients. In addition, chemotherapy affects estrogen levels in cancer patients. Estrogen levels are thought to have neuroprotective effects in the brain, thus helping to maintain cognitive function . Therefore, female cancer patients are more likely to develop cognitive impairment in brain regions related to learning and memory after chemotherapy, such as hippocampus and amygdala . The anterior cingulate cortex is involved in attention control, response selection and error monitoring . Abnormal brain activity patterns in the attention-controlled regions, including the anterior cingulate gyrus, are related with anxiety . The emotional fluctuation caused by excessive psychological stress in RC patients could induce abnormal activation of cingulate gyrus. Saykin, McDonald  revealed that the activation of frontal and parietal lobes increased during the speech working memory task 1 month after chemotherapy. Compared with controls, the cancer group showed significantly greater activation in right precentral gyrus, right cingulate gyrus . Moreover, in the SN, the nodal efficiency were only increased. We speculated that after surgery and chemotherapy, the node efficiency of SN showed more obvious activation in order to maintain robustness of overall network at the expense of other network property, such as integration. These results improved the understanding of chemotherapy-induced cognitive impairment in RC patients from the perspective of brain node efficiency.
No correlation between the nodal efficiency and HAMD score was found in the RC patients. We inferred that there was no significant result in correlation analysis due to the low HAMD score of patients, suggesting that depressive symptoms in RC patients are not obvious .
4.3 The difference of network resilience
In both networks, a key finding of significantly decreased resilience to targeted and random attack was found (Figure 4). Being more effective than other network properties to measure network integration performance, global efficiency of the FN and SN were utilized to explore network resilience quantitatively . In the present study, both networks of RC patients were more vulnerable and SN is less resilient than FN, which were consistent with our previous research results . This finding enhanced the conclusion that lower brain resilience was associated with progressive deterioration of cognitive impairment in breast cancer survivors . Similar results were investigated in other neurological diseases such as major depressive disorders  and temporal lobe epilepsy . A previous study showed that the degree distribution of brain network followed the exponentially truncated power law . This exponentially truncated power law distribution may be helpful in resisting the targeted attack of the hubs, meaning the brain networks of two groups were almost constant when deletion rate was low . The deletion ratios reaching 50%, the decline rate of global efficiency in networks began to exhibit obvious differences. Exploring the resilient of networks actually simulated the process of cognitive decline in all participants. In detail, as the important nodes were deleted, the functional and structural integrity of brain networks were impaired. Additionally, the FN was more resilient than the SN in present study, which were similar with these findings in previous studies [26, 60]. A prior study discovered that there was commonly a functional connectivity between regions that have no direct structural connectivity, implying that functional network was a more stable system in brain network . Therefore, functional networks were more robust to node removal. Our results may provide a new direction for studying cognitive impairment in RC patients after surgery and chemotherapy.