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Missing details or ambiguities about mathematical concepts and assumptions, algorithmic implementations, or parameterizations hinder progress. Such flaws are unfortunately frequent and one reason is a lack of readily applicable standards and tools for model description. Our work aims to advance complete and concise descriptions of network connectivity but also to guide the implementation of connection routines in simulation software and neuromorphic hardware systems. We first review models made available by the computational neuroscience community in the repositories ModelDB and Open Source Brain, and investigate the corresponding connectivity structures and their descriptions in both manuscript and code. The review comprises the connectivity of networks with diverse levels of neuroanatomical detail and exposes how connectivity is abstracted in existing description languages and simulator interfaces. We find that a substantial proportion of the published descriptions of connectivity is ambiguous. Based on this review, we derive a set of connectivity concepts for deterministically and probabilistically connected networks and also address networks embedded in metric space. Beside these mathematical and textual guidelines, we propose a unified graphical notation for network diagrams to facilitate an intuitive understanding of network properties. Examples of representative network models demonstrate the practical use of the ideas. We hope that the proposed standardizations will contribute to unambiguous descriptions and reproducible implementations of neuronal network connectivity in computational neuroscience.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010086","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T17:31:19Z","timestamp":1662658279000},"page":"e1010086","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":44,"title":["Connectivity concepts in neuronal network modeling"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6304-062X","authenticated-orcid":true,"given":"Johanna","family":"Senk","sequence":"first","affiliation":[]},{"given":"Birgit","family":"Kriener","sequence":"additional","affiliation":[]},{"given":"Mikael","family":"Djurfeldt","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6324-2600","authenticated-orcid":true,"given":"Nicole","family":"Voges","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9633-2573","authenticated-orcid":true,"given":"Han-Jia","family":"Jiang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7938-5967","authenticated-orcid":true,"given":"Lisa","family":"Sch\u00fcttler","sequence":"additional","affiliation":[]},{"given":"Gabriele","family":"Gramelsberger","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2308-5727","authenticated-orcid":true,"given":"Markus","family":"Diesmann","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7843-5993","authenticated-orcid":true,"given":"Hans E.","family":"Plesser","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0682-4855","authenticated-orcid":true,"given":"Sacha J.","family":"van Albada","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,9,8]]},"reference":[{"issue":"3","key":"pcbi.1010086.ref001","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1023\/A:1008925309027","article-title":"Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons","volume":"8","author":"N Brunel","year":"2000","journal-title":"Journal of Computational Neuroscience"},{"issue":"3","key":"pcbi.1010086.ref002","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.neuron.2020.01.040","article-title":"Systematic Integration of Structural and Functional Data into Multi-scale Models of Mouse Primary Visual Cortex","volume":"106","author":"YN Billeh","year":"2020","journal-title":"Neuron"},{"issue":"2","key":"pcbi.1010086.ref003","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.cell.2015.09.029","article-title":"Reconstruction and simulation of neocortical microcircuitry","volume":"163","author":"H Markram","year":"2015","journal-title":"Cell"},{"key":"pcbi.1010086.ref004","doi-asserted-by":"crossref","DOI":"10.3389\/fncom.2015.00120","article-title":"An algorithm to predict the connectome of neural microcircuits","volume":"9","author":"MW Reimann","year":"2015","journal-title":"Frontiers in Computational Neuroscience"},{"issue":"10","key":"pcbi.1010086.ref005","doi-asserted-by":"crossref","first-page":"e1006359","DOI":"10.1371\/journal.pcbi.1006359","article-title":"A multi-scale layer-resolved spiking network model of resting-state dynamics in macaque visual cortical areas","volume":"14","author":"M Schmidt","year":"2018","journal-title":"PLOS Computational Biology"},{"key":"pcbi.1010086.ref006","doi-asserted-by":"crossref","DOI":"10.3389\/fninf.2017.00030","article-title":"Constructing Neuronal Network Models in Massively Parallel Environments","volume":"11","author":"T Ippen","year":"2017","journal-title":"Frontiers in Neuroinformatics"},{"key":"pcbi.1010086.ref007","doi-asserted-by":"crossref","unstructured":"van Albada SJ, Morales-Gregorio A, Dickscheid T, Goulas A, Bakker R, Bludau S, et al. 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