Alzheimer's disease (AD) is the leading cause of intellectual impairment in the elderly worldwide 
. In its early stages, the most commonly recognized symptom is an inability to acquire new memories, such as difficulty in recalling recently observed facts, which is commonly referred to as the loss of episodic memory. As the disease progresses, extensive cognitive impairments begin to manifest, including language breakdown and long-term memory loss. Eventually, most brain functions deteriorate, ultimately leading to death. The neural basis underlying the functional damage is not yet fully understood. Recent studies based on multimodal imaging have provided evidence supporting the notion of AD as a disconnection syndrome 
Information interactions between interconnected brain regions are believed to be a basis of human cognitive processes 
. Networks have been used to model the brain and provide a new tool for understanding functional integration and segregation in the human brain and also the pathogenesis and treatment of neurological disorders 
. Elucidation of the complexity of brain networks will offer fundamental new insights into the general organizational principles of neurological functions from both global and integrative perspectives 
. Characterizing the underlying architecture of brain networks is an important issue in neuroscience.
Previous brain network studies of AD patients have revealed that their cognitive functional deficits may be due to abnormalities in the connectivity between different brain areas, although there is no consensus as to what the alteration pattern is 
. In 2007, using EEG data, Stam and colleagues found that although the network clustering coefficient was unchanged in AD patients, the patients displayed a longer characteristic path length 
. However, in 2008, using fMRI data, Supekar and colleagues found that AD patients had a lower clustering coefficient and no change in characteristic path length 
. In a structural imaging study the same year, He and colleagues found a higher clustering coefficient and longer characteristic path length in the brain structural networks of AD patients 
. In 2009, using MEG data, Stam and colleagues found a lower clustering coefficient and higher characteristic path length in the brain network in AD patients 
. Furthermore, in 2010, using resting-state fMRI data, Sanz-Arigita and colleagues found the clustering coefficient to be unchanged but a lower average shortest path in AD patients 
. In the same year, using structural MRI data, Yao and colleagues found a higher clustering coefficient and longer average shortest path length in AD patients; the authors also found that network topological measures in mild cognitive impairment (MCI) patients were between those of AD and NC groups 
. It should be noted that until now, studies of the altered brain network pattern in AD patients have not produced consistent results. With these studies, researchers do not obtain consistent results which may arise from the differences in the groups of subjects, different measurements and the image modalities used. As previously established, patients at different stages may manifest different behavioral symptoms with distinct underlying neural mechanisms 
. Thus, a study focused on a group of subjects with a specific disease stage (for example, mild, moderate or severe AD) will help us understand the network alteration in AD. In addition, the apolipoprotein E (ApoE) gene, located on chromosome 19, is a major susceptibility gene and is most clearly linked to late-onset AD. ApoE4 is the risk allele of the ApoE gene in AD 
. An increasing amount of evidence has indicated that ApoE4 modulates the brain activity of both normal aging and AD patients as measured by fMRI 
. However, to our knowledge, the question of whether the ApoE gene affects the topological properties of AD in the brain has not yet been studied.
In the current study, we specifically focused on moderate AD patients to directly investigate the hypothesis that the brain network of AD is characterized by the disruption of efficient small-world topological properties based on resting-state fMRI data. First, binary brain networks of individual brains were constructed with 90 brain regions as nodes extracted by an automated anatomical labeling (AAL) template 
with inter-regional functional connectivity as edges. Second, the topological parameters of the brain network (clustering coefficient, shortest path length, global efficiency and local efficiency) were evaluated at different connection densities. Third, statistical differences between the AD and NC groups were evaluated at both global and nodal levels. Finally, to evaluate the effects of genotype on global network properties, we compared network properties between NCs without ApoE4 and ApoE4− and ApoE4+ AD patients.