Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks—the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain—and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs.

Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks can be adequately modeled as random geometric graphs in hyperbolic spaces. In this paper, we present a computer program to generate such graphs. Besides real-world-like networks, the program can generate random graphs from other well-known graph ensembles, such as the soft configuration model, random geometric graphs on a circle, or Erdős-Rényi random graphs. The simulations show a good match between the expected values of different network structural properties and the corresponding empirical values measured in generated graphs, confirming the accurate behavior of the program.

In Parkinson's disease (PD), the luminance pattern electroretinogram (PERG) is reported to be abnormal, indicating dysfunction of retinal ganglion cells (RGCs). To determine the vulnerability of different subpopulations of RGCs in PD patients, the authors recorded the PERG to stimuli of chromatic (red-green [R-G] and blue-yellow [B-Y]) and achromatic (yellow-black [Y-Bk]) contrast, known to emphasize the contribution of parvocellular, koniocellular, and magnocellular RGCs, respectively. Subjects were early PD patients (n = 12; mean age, 60.1 +/- 8.3 years; range, 46 to 74 years) not undergoing treatment with levodopa and age-sex-matched controls (n = 12). Pattern electroretinograms were recorded monocularly in response to equiluminant R-G, B-Y, and Y-Bk horizontal gratings of 0.3 c/deg and 90% contrast, reversed at 1Hz, and presented at a viewing distance of 24 cm (59.2 x 59 degree field). In PD patients, the PERG amplitude was significantly reduced (by 40 to 50% on average) for both chromatic and luminance stimuli. Pattern electroretinogram latency was significantly delayed (by about 15 ms) for B-Y stimuli only. Data indicate that, in addition to achromatic PERGs, chromatic PERGs are altered in PD before levodopa therapy. Overall, chromatic PERGs to B-Y equiluminant stimuli exhibited the largest changes. Data are consistent with previous findings in PD, showing that visual evoked potentials (VEP) to B-Y chromatic stimuli are more delayed than VEPs to R-G and achromatic stimuli. The results suggest that the koniocellular subpopulation of RGCs may be particularly vulnerable in early stages of Parkinson's disease.

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Idiopathic Parkinson's disease (IPD) patients have abnormal visual evoked potentials (VEPs) and pattern electroretinograms (PERGs), attributed to dopaminergic transmission deficiency in visual pathway, probably the retina. VEP abnormalities are not reported in multiple system atrophy (MSA). The aim of this study was to investigate and compare chromatic (Ch) red-green (R-G) and blueyellow (B-Y), and luminance yellow-black (Y-Bk) PERGs in patients with MSA and IPD. We investigated 6 MSA patients (mean age: 62±7.4 years) not undergoing any pharmacological treatment, as well as 12 early IPD patients (mean age: 60.1±8.3 years) and 12 age-matched normal observers. ChPERGs were recorded monocularly in response to full-field equiluminant R-G, B-Y and Y-Bk horizontal gratings. In MSA only responses to R-G stimuli showed minimal insignificant changes (slight but not significant amplitude reduction without any significant latency delay); no significant abnormality was detected for B-Y and luminance Y-Bk stimuli. By contrast, in IPD all responses were reduced in amplitude and delayed in latency, above all for B-Y stimuli. Present data indicate that both chromatic and achromatic PERGs are virtually unaffected in MSA, whereas in early IPD they are clearly impaired, suggesting different pathogenic retinal mechanisms and a useful simple tool for distinguishing MSA from IPD.

The primate visual system is composed by two color-opponent pathways--red-green (R-G) and blue-yellow (B-Y)--subserved by the so-called parvo- and koniocellular streams respectively. The authors' aim was to compare the relative involvement of chromatic visual subsystems in multiple sclerosis (MS). In 30 MS patients with different forms of MS they recorded visual evoked potentials (VEPs) to onset (300 msec) and offset (700 msec) of equiluminant R-G and B-Y sinusoidal gratings of different contrast (90% and 25%). Equiluminance was established psychophysically by establishing the R-G and the B-Y color ratio at which chromatic gratings alternating at 15 and 10 Hz respectively had minimum visibility. The negative wave at stimulus onset with a peak latency of 120 to 160 msec was evaluated. Ordinary VEPs to luminance (LUM) contrast (black-white reversing checkerboards of 15' check size and 50% contrast) were also recorded for comparison. Latencies of R-G VEPs were abnormal in 53.3% and 58.3% of patients at 90% and 25% contrast respectively, whereas abnormal B-Y VEPs were 56.6% and 48.3%. Latencies of LUM VEPs were abnormal in 45% of patients. Interocular latency asymmetries were abnormal in 59.2% and 33.3% of patients for R-G, and 51.8% and 62.9% for B-Y. Latency asymmetries for LUM VEP were abnormal in 46.4% of patients. The higher rate of VEP abnormalities found with equiluminant chromatic stimuli compared with achromatic stimuli confirms the general vulnerability of color-opponent visual pathways in MS, even if the number of patients with abnormal findings was not significantly different when both test conditions were compared. VEPs to R-G and B-Y equiluminant stimuli appear to be involved approximately to the same extent.

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