We consider the problem of fuzzy community detection in networks, which complements and expands the concept of overlapping community structure. Our approach allows each vertex of the graph to belong to multiple communities at the same time, determined by exact numerical membership degrees, even in the presence of uncertainty in the data being analyzed. We create an algorithm for determining the optimal membership degrees with respect to a given goal function. Based on the membership degrees, we introduce a measure that is able to identify outlier vertices that do not belong to any of the communities, bridge vertices that have significant membership in more than one single community, and regular vertices that fundamentally restrict their interactions within their own community, while also being able to quantify the centrality of a vertex with respect to its dominant community. The method can also be used for prediction in case of uncertainty in the data set analyzed. The number of communities can be given in advance, or determined by the algorithm itself, using a fuzzified variant of the modularity function. The technique is able to discover the fuzzy community structure of different real world networks including, but not limited to, social networks, scientific collaboration networks, and cortical networks, with high confidence.
We explored the cortical pathways from the primary somatosensory cortex to the primary visual cortex (V1) by analysing connectional data in the macaque monkey using graph-theoretical tools. Cluster analysis revealed the close relationship of the dorsal visual stream and the sensorimotor cortex. It was shown that prefrontal area 46 and parietal areas VIP and 7a occupy a central position between the different clusters in the visuo-tactile network. Among these structures all the shortest paths from primary somatosensory cortex (3a, 1 and 2) to V1 pass through VIP and then reach V1 via MT, V3 and PO. Comparison of the input and output fields suggested a larger specificity for the 3a/1-VIP-MT/V3-V1 pathways among the alternative routes. A reinforcement learning algorithm was used to evaluate the importance of the aforementioned pathways. The results suggest a higher role for V3 in relaying more direct sensorimotor information to V1. Analysing cliques, which identify areas with the strongest coupling in the network, supported the role of VIP, MT and V3 in visuo-tactile integration. These findings indicate that areas 3a, 1, VIP, MT and V3 play a major role in shaping the tactile information reaching V1 in both sighted and blind subjects. Our observations greatly support the findings of the experimental studies and provide a deeper insight into the network architecture underlying visuo-tactile integration in the primate cerebral cortex.
Cognition is based on the integrated functioning of hierarchically organized cortical processing streams in a manner yet to be clarified. Because integration fundamentally depends on convergence and the complementary notion of divergence of the neuronal connections, we analysed integration by measuring the degree of convergence/divergence through the connections in the network of cortical areas. By introducing a new index, we explored the complementary convergent and divergent nature of connectional reciprocity and delineated the backward and forward cortical sub-networks for the first time. Integrative properties of the areas defined by the degree of convergence/divergence through their afferents and efferents exhibited distinctive characteristics at different levels of the cortical hierarchy. Areas previously identified as hubs exhibit information bottleneck properties. Cortical networks largely deviate from random graphs where convergence and divergence are balanced at low reciprocity level. In the cortex, which is dominated by reciprocal connections, balance appears only by further increasing the number of reciprocal connections. The results point to the decisive role of the optimal number and placement of reciprocal connections in large-scale cortical integration. Our findings also facilitate understanding of the functional interactions between the cortical areas and the information flow or its equivalents in highly recurrent natural and artificial networks.
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