[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-450326-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-450326-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","average-distance-between-the-processors-of-biswapped-networks","Average distance between the processors of biswapped networks","","Average distance metrics and transmission properties are analyzed for biswapped multiprocessor interconnection networks. The study constructs biswapped networks by systematically biswapping edges of a base graph while preserving connectivity and improving structural symmetry. Using distance sums from a given vertex to all others, the communication-cost indicator is linked to the Wiener index through a novel distance-based descriptor. Transmission values are further examined across biswapped networks derived from different base graphs, and the average node-to-node distance is compared.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/average-distance-between-the-processors-of-biswapped-networks/450326/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/average-distance-between-the-processors-of-biswapped-networks/450326.png","ImageObject",300,407,{"name":42,"@type":43},"Valentina","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-07","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What is the main network model studied in the document?","Question",{"text":62,"@type":63},"The document studies biswapped multiprocessor interconnection networks constructed by biswapping edges of a base graph while preserving connectivity and enhancing symmetry.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How is communication cost related to distance in biswapped networks?",{"text":67,"@type":63},"Communication cost is connected to the sum of distances from a particular node to all other nodes, which is used to compute a novel distance-based descriptor based on the Wiener index.",{"name":69,"@type":60,"acceptedAnswer":70},"What additional analysis is performed beyond average distance?",{"text":71,"@type":63},"Transmission values of biswapped networks are analyzed for networks derived from various base graphs, and the average distance between nodes is investigated across those constructions.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},450326,1791156864,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},8,30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145},13056703020460,"https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923","[www. nature.com/scientificreports](www. nature.com/scientificreports)  \nOPEN  \nAverage distance between the processors of biswapped networks  \nS. Prabhu1, M. Anitha1􀀍, N. Harish Vidyarth2 & Paul Manuel3  \nBiswapped networks provide an efficient way to interconnect nodes through transpose like operations that balance both connectivity and performance. A biswapped network is constructed by systematically biswapping edges within a base graph G, thereby preserving essential connectivity properties while enhancing structural symmetry. This improved symmetry contributes to fault tolerance and energy efficiency, making biswapped networks a promising model for robust network design. In this study, we investigate the sum of distances from a particular node to all others, the transmission of a node in a biswapped network, which is a key indicator of communication cost which helps to compute the novel distance based descriptor Wiener index. Furthermore, we analyze transmission values of biswapped networks derived from various base graphs. Finally, the average distance between the nodes of biswapped networks constructed by various base graphs were investigated.  \nKeywords Transmission, Vertex transitive, Hypercube, Biswapped network  \nMultiprocessor interconnection networks are becoming a must-have for parallel microprocessing architectures because they are cost effective, highly versatile and allowing them to be utilized in numerous ways for efficient data transfer, task distribution and resource sharing. The fast growth of these networks, driven by decentralization and adaptive scalability, shows how important it is to look at and improve their design. When studying a wellstructured graph network G = (V, E), there are several ways to measure the distance between the entities of the network. These distances can be considered between individual vertices, between edges, vertex to edges, or even between larger subgraphs. Examining these distances elucidates the connectivity of the network and offers insight into potential structural changes over time. A prevalent method involves computing the shortest route distance, denoted as d(u, v), which represents the minimal number of steps or the least cost required to go from node u to node v. Identifying these shortest pathways not only elucidates the most efficient routes inside the network but also enhances our comprehension of its general structure and dynamics. The notations used in this paper are summarized in Table 1.  \nFor S ⊆ V, d (S, v) = min d(v, x). If H is a subgraph of G, then d(v, H) = min d (v, x) . This provides x∈S x∈V(H)  \ninsight into how a single vertex relates to a group, helpful in clustering and influence spread studies. A subgraph H is said to be isometric, if d (u, v) = dH (u, v) . A graph X is vertex-transitive if for every pair of vertices u, v ∈ V (X), there exists an automorphism φ in the automorphism group Aut(X) such that φ (u) = v. In other words, the automorphism group of X acts transitively on V(X), meaning that all vertices are structurally equivalent under symmetry transformations. We refer, [τ] = {1, 2 ,... ,τ} and [τ]0 = {0, 1 , 2 ,... ,τ} . Also to connote {τ +1,τ +2 , . . . , 2τ +1} we refer the notation [2τ + 1] − [τ] .  \nHypercube commonly known as τ-cube (denoted by Qτ ) is a versatile interconnection network which is a predominant example of a network which posses a distance preserving subgraphs, commonly used by the computer scientists for its structure symmetry, scalability and fault-tolerant operational systems1. It is defined by the renowned operation named to be Cartesian product. That is Qτ = K2 × K2 × · · · × K2 (τ times) . The number of vertices is one of the most interesting things about a hypercube. A hypercube with τ dimensions has 2τ corners. This is because each vertex is linked to a different binary string of length τ, with each bit being  \neither 0 or 1. As a result, increasing property is the number of edges. An  \nthe dimension by τ-cube","cbCaihhZGOfiKL9q","https://ap.wps.com/l/cbCaihhZGOfiKL9q","pdf",3220746,13,"English","# Overview\n## Biswapped networks and construction\n## Distance measures and communication cost\n## Vertex-transitive and symmetry concepts\n# Hybercube background\n## Definition and properties of Qτ\n## Nomenclature and notation\n# Network variants","[{\"question\":\"What is the main network model studied in the document?\",\"answer\":\"The document studies biswapped multiprocessor interconnection networks constructed by biswapping edges of a base graph while preserving connectivity and enhancing symmetry.\"},{\"question\":\"How is communication cost related to distance in biswapped networks?\",\"answer\":\"Communication cost is connected to the sum of distances from a particular node to all other nodes, which is used to compute a novel distance-based descriptor based on the Wiener index.\"},{\"question\":\"What additional analysis is performed beyond average distance?\",\"answer\":\"Transmission values of biswapped networks are analyzed for networks derived from various base graphs, and the average distance between nodes is investigated across those constructions.\"}]","Average distance between the processors of biswapped networks | PDF",1790732897,33]