Isotopy and energy of physical networks

Liu, Yanchen; Dehmamy, Nima; Barabási, Albert László

doi:10.1038/s41567-020-1029-z

Cited by 22 publications

(23 citation statements)

References 27 publications

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“…Modularity-based network community detection [9,10,12] is arguably the most popular framework for identifying communities in networks, partly because of its already established status quo including various numerical tools on top of its mathematically intuitive interpretation of detecting densely connected subsets of nodes. The most widely used type of modularity function for a given community partition {g i } ( g i represents the community identity of node i) is given by where the adjacency matrix elements A ij represent the existence of an edge between nodes i and j ( A ij = 1 if the edge exists and A ij = 0 if it does not), 4 and the degree k i represents the number of neighbors of node i and is given by…”

Section: Modified Null-model Term For Bipartite Networkmentioning

confidence: 99%

“…On the way to reality, however, they have encountered various types of constraints imposed in different systems. For instance, a network may represent relations in a physical space where one must take spatial constraints into account [4], e.g., spatial networks [5] with physical restrictions such as the no edge-crossing rule [6]. One of the most prominent types of networks with such restrictions is the bipartite network [1,7]: a network composed of two distinct groups of nodes, where edges can only connect nodes belonging to different groups.…”

Section: Introductionmentioning

confidence: 99%

“…For the record, the present work includes the result of re-analyzing the data used in Ref [19]. and its implication 4. We only consider undirected networks with A ij = A ji for every node pairs (i, j), as the concept of communities in directed networks can be quite nontrivial.…”

mentioning

confidence: 99%

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Refinement for community structures of bipartite networks

Lee

2021

J. Korean Phys. Soc.

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Bipartite networks composed of dichotomous node sets are ubiquitous in nature and society. Partly for simplicity's sake, many studies have focused on their projection onto their unipartite versions where one only needs to care about a single type of node. When it comes to mesoscale structures such as communities, however, properly incorporating a priori structural restrictions such as bipartivity is ever more important. In this paper, as a case study, we take the community structure of bipartite networks in various scales to examine the amount of information of bipartivity encoded in the community detection procedure. In particular, we report the robustness in reliability of detected community based on consistency by comparing the detection algorithm with or without the consideration of bipartivity. From the analysis with model networks embedding prescribed communities and real networks, we find that the community detection tailored to take the bipartivity into account clearly yields more robust community structures than the one without such structural information. This demonstrates the necessity for customizing the community detection algorithm by encoding whatever information is known about networks of interest and, at the same time, raises an interesting question on the possibility of estimating the quantitative amount of information from such a customization.

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Section: Modified Null-model Term For Bipartite Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Refinement for community structures of bipartite networks

Lee

2021

J. Korean Phys. Soc.

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“…Recent research into large networks, such as the brain, has focused on the threedimensional layout of the network, which affects the structure and function of the system. The results of [2] allow formulating a statistical model for the formation of tangles in physical networks, with finding that the mouse connectome is more entangled than expected based on optimal wiring. In [3], general hierarchical models of consciousness were constructed, including equations governing the cooperative variables for several cognitive modalities: semantic and working memory, attention, emotion, perception, and their sequential interaction.…”

Section: Introductionmentioning

confidence: 99%

Hypothesis of Cyclic Structures of Pre- and Consciousness as a Transition in Neuron-like Graphs to a Special Type of Symmetry

Аристов

Stepanyan

2022

Symmetry

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We study the proposed statistical kinetic model for describing the pre- and consciousness structures based on the cognitive neural networks. The method of statistics of the growth graph systems and a possible transition to symmetric structures (a kind of phase transition) is applied. With the complication of a random Erdőos-Rényi (ER) graph during the percolation transition from the tree structure to the large cluster structures is obtained. In the evolutionary model two classes of algorithms have been developed. The differences between the cycle parameters in the obtained neural network models can reach thousands or more times. This is due to the tree-like architecture of the neural graph, which mimics the columnar structures of the neocortex. These cluster and cyclic structures can be interpreted as the primary elements of consciousness and as a necessary condition for the effect of consciousness itself. The comparison with other known theoretical mainly statistical models of consciousness is discussed. The presented results are promising in neurocomputer interfaces, man-machine systems and artificial intelligence systems.

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“…On the way to reality, however, they have encountered various types of constraints imposed in different systems. For instance, a network may represent relations in the physical space where one must take spatial constraints into account [4], e.g., spatial networks [5] with physical restrictions such as no edge-crossing rule [6]. One of the most prominent types of networks with such restrictions is the bipartite network [1,7]: the networks composed of two distinct groups of nodes, where edges can only connect nodes belonging to different groups.…”

Section: Introductionmentioning

confidence: 99%

Refinement for community structures of bipartite networks

Lee

2021

Preprint

View full text Add to dashboard Cite

Bipartite networks composed of dichotomous node sets are ubiquitous in nature and society. Partly for the simplicity's sake, many studies have focused on their projection onto their unipartite versions where one only needs to care about a single type of nodes. When it comes to mesoscale structures such as communities, however, it is ever more important to properly incorporate a priori structural restrictions such as bipartivity. In this paper, as a case study, we take the community structure of bipartite networks in various scales to examine the amount of information of bipartivity encoded in the community detection procedure. In particular, we report the robustness in reliability of detected community based on consistency by comparing the detection algorithm with or without the consideration of bipartivity. From the analysis with model networks embedding prescribed communities and real networks, we find that the community detection tailored to take the bipartivity into account clearly yields more robust community structures than the one without utilizing such structural information. Therefore, it demonstrates the necessity for customizing the community detection algorithm encoding whatever information known about networks of interest, and at the same time it raises an interesting question on the possibility of estimating the quantitative amount of information from such customization.

show abstract

Isotopy and energy of physical networks

Cited by 22 publications

References 27 publications

Refinement for community structures of bipartite networks

Refinement for community structures of bipartite networks

Hypothesis of Cyclic Structures of Pre- and Consciousness as a Transition in Neuron-like Graphs to a Special Type of Symmetry

Refinement for community structures of bipartite networks

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