## 1 Introduction  
Alzheimer's disease (AD) is the most widespread neurodegenerative disorder and is a growing health problem. It is mainly characterized by short-term memory loss in its earlier stages, followed by a progressive decline in other cognitive and behavioural functions as the disease advances [1]. Investigating useful _biomarkers_ for the early diagnosis, prognosis and response to therapy is one of the primary goals of the current research activity in neuroscience. A number of studies provided evidence that the decline due to AD is related to a disrupted connectivity among brain regions, caused by white matter (WM) degeneration, e.g., [2, 3]. Due to their homogeneous chemical composition, conventional MRI is not able to highlight the structure of the WM fibers, therefore, it is not tailored to investigate the physical disconnections arising among them. Conversely, a promising technique for such an investigation is diffusion weighted imaging (DWI). This technique, in fact, is able to analyze the WM micro-structural integrity and can thus help identify WM alterations that may occur due to AD [4]. Different approaches have been proposed to study the diagnostic potential of DWI data, ranging from a finer voxelwise analysis [5] to an ROI-based approach [6]. In the last few years, a growing interest has arisen towards the application of an alternative approach based on complex network theory. When combined with tractography algorithms [7], in fact, DWI enables the reconstruction of the WM fiber tracts, providing a characterization of the physical connections of the brain that can be subsequently investigated through a complex network-based approach [8]. More precisely, the brain can be modeled as a network whose nodes are the anatomical regions and whose edges are related to the fiber tracts connecting them. Traditional network metrics suitable for describing topological properties of the brain include nodal degree and strength, and shortest path length. In particular, a very promising research direction consists in feeding graph-based topological measures into machine learning algorithms so as to automatize the disease detection, e.g., [9; 10; 11]. Developing computer aided diagnosis systems is desirable, as they can provide a non-invasive, low-cost tool-support to the traditional neuropsychological assessment performed by expert clinicians. Moreover, a great variety of state-of-the-art machine learning approaches, has shown outstanding performance for early detection and automated classification of Alzheimer's disease (AD) [12; 13]. Recently, we investigated the usefulness in this context of an uncommon graph measure, that is _communicability_. Communicability quantifies the ease of communications between node pairs in a network by considering not only the shortest path connecting them, but all possible available routes [14]. For this reason, this metric revealed to be particularly sensitive to the disruption of communication between brain regions due to AD [15; 16]. In [15], communicability was able to outperform more classic graph measures on a mixed cohort of healthy control (HC) subjects and AD patients from the public Alzheimer's Disease Neuroimaging Initiative (ADNI) database ([[http://adni.loni.usc.edu/](http://adni.loni.usc.edu/)]([http://adni.loni.usc.edu/](http://adni.loni.usc.edu/))). Since the main goal was to compare communicability to other classic measures, we fixed the classification model to be used, i.e., support vector machines. Furthermore, a cortical parcellation scheme was adopted for the estimated brain networks. On one hand, the use of only one classifier may be not enough to claim the robustness of the communicability-based approach for supporting the automatic disease detection. On the other hand, the use of a coarse anatomical scheme could have overlooked detailed patterns of connectivity, which may play a key role in neurological diseases investigation.