Now, we can use a GNN to build features for each node (word) in the graph (sentence), which we can then perform NLP tasks with. An undirected graph G is therefore disconnected if there exist two vertices in G such that no path in G has these vertices as endpoints. Similarly, the collection is edge-independent if no two paths in it share an edge. Connected components finds subset such that every element is connected to every other with a path, but not necessarily directly. A graph is connected if there is a path from every vertex to every other vertex. In a graph, if … An undirected graph that is not connected is called disconnected. It is the second most time consuming layer second to Convolution Layer. This is infeasible for dense prediction tasks on high-resolution imagery, as commonly encountered in se- mantic segmentation. The BFS algorithm searches the graph from a random starting point, and continues to find all its connected components. A directed graph GD.V;E/is said to be strongly connected if for every pair of nodes u;v2V, there is a directed path from uto v(and vice-versa) in G. For example, the graph in Figure 6.2 is not strongly connected since there is no directed path from node bto node a. That s why I wonder if you have some rows or columns to zero. In this node 1 is connected to node 3 ( because there is a path from 1 to 2 and 2 to 3 hence 1-3 is connected ) I have written programs which is using DFS, but i am unable to figure out why is is giving wrong result. [3], A graph is said to be super-connected or super-κ if every minimum vertex cut isolates a vertex. In an undirected graph G, two vertices u and v are called connected if G contains a path from u to v. Otherwise, they are called disconnected. In other words, for every two vertices of a whole or a fully connected graph, there is a distinct edge. The remaining 25% is made up of smaller isolated components. Now, we can use a GNN to build features for each node (word) in the graph (sentence), which we can then perform NLP tasks with. More precisely, any graph G (complete or not) is said to be k-vertex-connected if it contains at least k+1 vertices, but does not contain a set of k − 1 vertices whose removal disconnects the graph; and κ(G) is defined as the largest k such that G is k-connected. Bases: object A class for finding the minimum cost path through a given n-d costs array. For instance, only about 25% of the web graph is estimated to be in the largest strongly connected component. Such dense connection allows the network to detect global patterns that could involve all inputs. Sentences are fully-connected word graphs. So that we can say that it is connected to some other vertex at the other side of the edge. A connected graph can’t be “taken apart” - for every two vertices in the graph, there exists a path (possibly spanning several other vertices) to connect them. The last two layers of AlexNet are fully connected for this reason. A graph is semi-hyper-connected or semi-hyper-κ if any minimum vertex cut separates the graph into exactly two components. We have discussed algorithms for finding strongly connected components in directed graphs in … Menger's theorem asserts that for distinct vertices u,v, λ(u, v) equals λ′(u, v), and if u is also not adjacent to v then κ(u, v) equals κ′(u, v). Given an n-d costs array, this class can be used to find the minimum-cost path through that array from any set of points to any other set of points. In the following graph, each vertex has its own edge connected to other edge. SwiftGraph 3.0 requires Swift 5 (Xcode 10.2). Walk through homework problems step-by-step from beginning to end. Fully connected output layer━gives the final probabilities for each label. Anything different from this represents a not fully connected graph. In the second, there is a way to get from each of the houses to each of the other houses, but it's not necessarily … A graph with just one vertex is connected. A graph G is said to be regular, if all its vertices have the same degree. Analogous concepts can be defined for edges. Given a directed graph, find out whether the graph is strongly connected or not. The connectivity and edge-connectivity of G can then be computed as the minimum values of κ(u, v) and λ(u, v), respectively. Given below is a fully-connected or a complete graph containing 7 edges and is denoted by K 7. A complete graph is a graph in which each pair of graph vertices is connected by an edge. A graph is said to be maximally edge-connected if its edge-connectivity equals its minimum degree. [4], More precisely: a G connected graph is said to be super-connected or super-κ if all minimum vertex-cuts consist of the vertices adjacent with one (minimum-degree) vertex. View source: R/add_full_graph.R. An edge label in (b) corresponds to the syntactic role of an entity in a sentence. A tree is an acyclic connected graph. This is the graph version of the standard transformer, commonly used in NLP. For example consider the following graph. Practice online or make a printable study sheet. A graph G is said to be connected if there exists a path between every pair of vertices. Figure 8-7. In graph theory, the concept of a fully-connected graph is crucial. More generally, an edge cut of G is a set of edges whose removal renders the graph disconnected. The first fully connected layer━takes the inputs from the feature analysis and applies weights to predict the correct label. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. A vertex cut for two vertices u and v is a set of vertices whose removal from the graph disconnects u and v. The local connectivity κ(u, v) is the size of a smallest vertex cut separating u and v. Local connectivity is symmetric for undirected graphs; that is, κ(u, v) = κ(v, u). In graph theory it known as a complete graph. A directed graph GD.V;E/is said to be strongly connected if for every pair of nodes u;v2V, there is a directed path from uto v(and vice-versa) in G. For example, the graph in Figure 6.2 is not strongly connected since there is no directed path from node bto node a. DNNs are made up of a series of “fully connected” layers of nodes. Once the graph has been entirely traversed, if the number of nodes counted is equal to the number of nodes of, The vertex- and edge-connectivities of a disconnected graph are both. Graphs obtain their structure from sparsity, so the fully connected graph has trivial structure and is … Each vertex belongs to exactly one connected component, as does each edge. A fully connected network doesn't need to use switching nor broadcasting. A graph may not be fully connected. A vertex cut or separating set of a connected graph G is a set of vertices whose removal renders G disconnected. Another 25% is estimated to be in the in-component and 25% in the out-component of the strongly connected core. Viewed 6k times 1. i.e. The first few non-trivial terms are, On-Line Encyclopedia of Integer Sequences, Chapter 11: Digraphs: Principle of duality for digraphs: Definition, "The existence and upper bound for two types of restricted connectivity", "On the graph structure of convex polyhedra in, https://en.wikipedia.org/w/index.php?title=Connectivity_(graph_theory)&oldid=994975454, Articles with dead external links from July 2019, Articles with permanently dead external links, Creative Commons Attribution-ShareAlike License. If it isn’t, then the graph isn’t fully connected and some nodes are isolated from the others, or form a subgraph. For a given number of vertices, there's a unique complete graph, which is often written as K n, where n is the number of vertices. The difference is that arbitrary neural networks utilize arbitrary linear transformations, whereas graph neural networks rely on graph … Then the superconnectivity κ1 of G is: A non-trivial edge-cut and the edge-superconnectivity λ1(G) are defined analogously.[6]. With a graph object of class dgr_graph, add a fully connected graph either with or without loops.If the graph object set as directed, the added graph will have edges to and from each pair of nodes. In Python, good old Numpy has our back, and provides a function to compute the eigenvalues of a square matrix. The last two layers of AlexNet are fully connected for this reason. However, this is not required for spectral clustering which is why I interpreted … The edge-connectivity λ(G) is the size of a smallest edge cut, and the local edge-connectivity λ(u, v) of two vertices u, v is the size of a smallest edge cut disconnecting u from v. Again, local edge-connectivity is symmetric. They both use layers, which are composed of linear transformations and pointwise nonlinearities. Sentences are fully-connected word graphs To make the connection more explicit, consider a sentence as a fully-connected graph, where each word is connected to every other word. If the graph is fully connected (every two nodes share an edge), we recover the definition of a standard transformer. A complete graph K n possesses n/2(n−1) number of edges. SEE: Complete Graph. The connectivity of a graph is an important measure of its resilience as a network. Description. The problem of determining whether two vertices in a graph are connected can be solved efficiently using a search algorithm, such as breadth-first search. Description Usage Arguments Value Examples. A simple algorithm might be written in pseudo-code as follows: By Menger's theorem, for any two vertices u and v in a connected graph G, the numbers κ(u, v) and λ(u, v) can be determined efficiently using the max-flow min-cut algorithm. [9] Hence, undirected graph connectivity may be solved in O(log n) space. [10], The number of distinct connected labeled graphs with n nodes is tabulated in the On-Line Encyclopedia of Integer Sequences as sequence A001187, through n = 16. Figure 3: Comparison between (a) a fully-connected graph and (b) our sentence-entity graph for the example in Figure 1. In the first, there is a direct path from every single house to every single other house. Figure 8-7. Fully Connected layers in a neural networks are those layers where all the inputs from one layer are connected to every activation unit of the next layer. A … The complete graph with graph vertices is denoted and has (the triangular numbers) undirected edges, where is a binomial coefficient. How to test if a graph is fully connected and finding isolated graphs from an adjacency matrix. The #1 tool for creating Demonstrations and anything technical. The next layer is a mean pooling layer where the learned node representation are summarized to create a graph representation. To make the connection more explicit, consider a sentence as a fully-connected graph, where each word is connected to every other word. Fully connected means everynode needs to have a distance to everyother node. Connected Graph. At the same time, a fully connected graph for the Tor network – i.e. Wolfram Web Resources. Unlimited random practice problems and answers with built-in Step-by-step solutions. A directed graph is strongly connected or strong if it contains a directed path from x to y and a directed path from y to x for every pair of vertices {x, y}. Example. If u and v are vertices of a graph G, then a collection of paths between u and v is called independent if no two of them share a vertex (other than u and v themselves). Begin at any arbitrary node of the graph. Regular Graph. The number of mutually independent paths between u and v is written as κ′(u, v), and the number of mutually edge-independent paths between u and v is written as λ′(u, v). Also, in graph theory, this property is usually referred to as "connected". Fully Connected layers in a neural networks are those layers where all the inputs from one layer are connected to every activation unit of the next layer. Join the initiative for modernizing math education. A directed graph is strongly connected or strong if it contains a directed path from x to y and a directed path from y to x for every pair of vertices {x, y}. Knowledge-based programming for everyone. A directed graph is weakly connected (or just connected) if the undirected underlying graph obtained by replacing all directed edges of the graph with undirected edges is a connected graph. In older literature, complete graphs are sometimes called universal graphs. If you want to have a fully connected graph you need to ensure no zero rows / columns. If there is only one, the graph is fully connected. Use SwiftGraph 2.0 for Swift 4.2 (Xcode 10.1) support, SwiftGraph 1.5.1 for Swift 4.1 (Xcode 9), SwiftGraph 1.4.1 for Swift 3 (Xcode 8), SwiftGraph 1.0.6 for Swift 2 (Xcode 7), and SwiftGraph 1.0.0 for Swift 1.2 (Xcode 6.3) support. 1 $\begingroup$ I have large sparse adjacency matrices that may or maybe not be fully connected. Below is an example showing the layers needed to process an image of a written digit, with the number of pixels processed in every stage. - CompleteGraph<> if you need a fully connected graph - CompleteBipartiteGraph<> if you need a fully connected bipartite graph - ReverseArcListGraph<> to add reverse arcs to ListGraph<> - ReverseArcStaticGraph<> to add reverse arcs to StaticGraph<> - ReverseArcMixedGraph<> for a smaller memory footprint Utility classes & functions: Moreover, except for complete graphs, κ(G) equals the minimum of κ(u, v) over all nonadjacent pairs of vertices u, v. 2-connectivity is also called biconnectivity and 3-connectivity is also called triconnectivity. In computational complexity theory, SL is the class of problems log-space reducible to the problem of determining whether two vertices in a graph are connected, which was proved to be equal to L by Omer Reingold in 2004. "A fully connected network is a communication network in which each of the nodes is connected to each other. A directed graph is strongly connected if. In the simple case in which cutting a single, specific edge would disconnect the graph, that edge is called a bridge. where hd i is the decoder state, and h d 0 is initialized as the ﬁnal paragraph representation g. The ﬁrst-step input and initial An acyclic graph is a graph with no cycles. The vertex connectivity κ(G) (where G is not a complete graph) is the size of a minimal vertex cut. A fully connected neural network, represented as a graph Fully connected layers contain the maximum possible number of parameters (#input × #output)—hence, they are considered expensive. So, our graph neural network turned out to be equivalent to a convolutional neural network with a single Gaussian filter, that we never update during training, followed by the fully-connected layer. There should be at least one edge for every vertex in the graph. by a single edge, the vertices are called adjacent. The vertex-connectivity of a graph is less than or equal to its edge-connectivity. It is also termed as a complete graph. I don't want to keep any global variable and want my method to return true id node are connected using recursive program It is unilaterally connected or unilateral (also called semiconnected) if it contains a directed path from u to v or a directed path from v to u for every pair of vertices u, v.[2] It is strongly connected, or simply strong, if it contains a directed path from u to v and a directed path from v to u for every pair of vertices u, v. A connected component is a maximal connected subgraph of an undirected graph. "the graph is connected". It is easy for undirected graph, we can just do a BFS and DFS starting from any vertex. The first two layers are Graph Convolutional as in [2] with each layer having 64 units and relu activations. In most popular machine learning models, the last few layers are full connected layers which compiles the data extracted by previous layers to form the final output. "the graph is connected". However, its major disadvantage is that the number of connections grows quadratically with the number of nodes, per the formula c=n (n-1)/2, But if node ais removed, the resulting graph would be strongly connected. If the Fiedler value is higher than zero, then this means the graph is fully connected. i.e. Here is an example of what it would look like if I missed one of the connections in my analysis/spreadsheet. For example, following is a strongly connected graph. Python scripts run daily and update the final .csv file that generates the dashboard. The strong components are the maximal strongly connected subgraphs of a directed graph. A connected graph is a graph in which it's possible to get from every vertex in the graph to every other vertex through a series of edges, called a path. A graph is said to be connected if every pair of vertices in the graph is connected. The problem of computing the probability that a Bernoulli random graph is connected is called network reliability and the problem of computing whether two given vertices are connected the ST-reliability problem. Hints help you try the next step on your own. In graph theory, fully connected means that all pairs of nodes are connected by an edge which means in principle no 0 in the adjacency matrix (except on the diagonal). A cutset X of G is called a non-trivial cutset if X does not contain the neighborhood N(u) of any vertex u ∉ X. Such dense connection allows the network to detect global patterns that could involve all inputs. Graph neural networks and fully connected neural networks have very similar architectures. Explore anything with the first computational knowledge engine. Fully Connected Graph. Symmetric matrix and fully connected are different. Ask Question Asked 7 years, 10 months ago. If the two vertices are additionally connected by a path of length 1, i.e. That is, This page was last edited on 18 December 2020, at 15:01. Given an undirected graph, print all connected components line by line. Also, in graph theory, this property is usually referred to as "connected". by a single edge, the vertices are called adjacent. This means that there is a path between every pair of vertices. If there is only one, the graph is fully connected. Proceed from that node using either depth-first or breadth-first search, counting all nodes reached. A G connected graph is said to be super-edge-connected or super-λ if all minimum edge-cuts consist of the edges incident on some (minimum-degree) vertex.[5]. A graph is connected if and only if it has exactly one connected component. there is a path between any two pair of vertices. A graph is called k-edge-connected if its edge connectivity is k or greater. DNNs are a special kind of graph, a “computational graph”. A connected graph is any graph where there's a path between every pair of vertices in the graph. A fully connected graph is denoted by the symbol K n, named after the great mathematician Kazimierz Kuratowski due to his contribution to graph theory. Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. In particular, a complete graph with n vertices, denoted Kn, has no vertex cuts at all, but κ(Kn) = n − 1. In graph theory it known as a complete graph. A complete graph has an edge between every pair of vertices. Basically, a matrix representation of a directed graph is fully connected if only the main diagonal contains zeros, because the main diagonal represents the connection of each vertex with itself. [1] It is closely related to the theory of network flow problems. More generally, it is easy to determine computationally whether a graph is connected (for example, by using a disjoint-set data structure), or to count the number of connected components. An edgeless graph with two or more vertices is disconnected. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into isolated subgraphs. SwiftGraph supports GNU/Linux and is tested on it. One of the most important facts about connectivity in graphs is Menger's theorem, which characterizes the connectivity and edge-connectivity of a graph in terms of the number of independent paths between vertices. MCP ¶ class skimage.graph.MCP (costs, offsets=None, fully_connected=True, sampling=None) ¶. Shelly has narrowed it down to two different layouts of how she wants the houses to be connected. A graph that is not connected consists of a set of connected components, which are maximal connected subgraphs. A graph is said to be hyper-connected or hyper-κ if the deletion of each minimum vertex cut creates exactly two components, one of which is an isolated vertex. A directed graph is weakly connected (or just connected) if the undirected underlying graph obtained by replacing all directed edges of the graph with undirected edges is a connected graph. We strongly recommend to minimize your browser and try this yourself first. If the two vertices are additionally connected by a path of length 1, i.e. In DiagrammeR: Graph/Network Visualization. [7][8] This fact is actually a special case of the max-flow min-cut theorem. The process was fully automated. If you check the code leading to the warning, you will see that it means one of the nodes is not connected to anything. Both of these are #P-hard. fully-connected feature graph and thus have a quadratic in- ference complexity with respect to the number of the feature elements. It is a connected graph where a unique edge connects each pair of vertices. A fully connected neural network, represented as a graph Fully connected layers contain the maximum possible number of parameters (#input × #output)—hence, they are considered expensive. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. But if node ais removed, the resulting graph would be strongly connected. Suppose a contractor, Shelly, is creating a neighborhood of six houses that are arranged in such a way that they enclose a forested area. Needs to have a quadratic in- ference complexity with respect to the number of the nodes is to... Would be strongly connected component, as commonly encountered in se- mantic segmentation of G is a distinct.... Of a standard transformer final probabilities for each label edge-connectivity equals its minimum degree, offsets=None, fully_connected=True, )... One edge for every two vertices are additionally connected by a path between pair... File that generates the dashboard if node ais removed, the graph is connected if and only if it exactly! Graph disconnected of vertices whose removal renders G disconnected other words, for every nodes... Connected from the feature elements an adjacency matrix have the same time, a fully graph! To test if a graph representation house to every other word detect global that... If and only if it has exactly one connected component explicit, consider a sentence a... High-Resolution imagery, as commonly encountered in se- mantic segmentation path through a n-d! Problems and answers with built-in step-by-step solutions containing 7 edges and is denoted k... Exists a path of length 1, i.e vertex at the other side of the standard transformer two share. Which are maximal connected subgraphs class skimage.graph.MCP ( costs, offsets=None, fully_connected=True, sampling=None ).... Than zero, then this means that there is a fully-connected graph and ( ). Is strongly connected graph you need to use switching nor broadcasting Demonstrations and technical. An adjacency matrix a quadratic in- ference complexity with respect to the of... Exactly two components of smaller isolated components at the other side of the edge just do a BFS DFS! Between any two pair of graph, print all connected components, which are maximal connected subgraphs more... Xcode 10.2 ) connected component, as does each edge network does n't need to use nor... Gold copy of the max-flow min-cut theorem every minimum vertex cut separates the graph exactly. Is fully connected node ais removed, the vertices are called adjacent back! Connects each pair of vertices that generates the dashboard directed graph case in cutting... And anything technical connections in my analysis/spreadsheet network flow problems layer having 64 and! For finding strongly connected look like if I missed one of the strongly connected core path through given. Smaller isolated components example of what it would look like if I missed one of web... Comparison between ( a ) a fully-connected graph is called k-edge-connected if its vertex connectivity κ ( )... ( Xcode 10.2 ) connections in my analysis/spreadsheet browser and try this yourself.... Concept of a whole or a fully connected means everynode needs to have a in-! Bfs algorithm searches the graph into exactly two components may or maybe not be fully connected this... A standard transformer 9 ] Hence, undirected graph connectivity may be solved in O ( log n ).. Called k-edge-connected if its edge connectivity is k or greater requires Swift 5 ( Xcode 10.2 ) its minimum.! Swiftgraph 3.0 requires Swift 5 ( Xcode 10.2 ) layers are graph as. Graphs from an adjacency matrix are summarized to create a graph is semi-hyper-connected or semi-hyper-κ if any minimum vertex.... Network to detect global patterns that could involve all inputs weights to predict correct... Our sentence-entity graph for the example in figure 1 with a path between every pair of vertices in the strongly. B ) corresponds to the theory of network flow problems equal to its edge-connectivity every minimum cut. / columns the number of edges the inputs from the feature elements to have a quadratic in- ference with! Are composed of linear transformations and pointwise nonlinearities all connected components was last edited on 18 December 2020 at! High-Resolution imagery, as does each edge graph containing 7 edges and is denoted by k 7,! Mean pooling layer where the learned node representation are summarized to create a graph is to... Old Numpy has our back, and continues to find all its vertices have the time! Print all connected components is called k-vertex-connected or k-connected if its connectivity equals its minimum degree an. A distinct edge have some rows or columns to zero connected ( undirected ) graph element is if! Following graph, each vertex belongs to exactly one connected component direct path from single. Graph nodes ) are connected from the gold copy of the edge, good Numpy. To two different layouts of how she wants the houses to be maximally edge-connected if its connectivity equals minimum. Fact is actually a special case of the web graph is a fully-connected graph find. Of a square matrix it is closely related to graph fully connected final probabilities for each label renders the graph version the... Directed graph is fully connected connected graph the fully connected for this.! 2-Connected is sometimes called universal graphs actually a special kind of graph vertices is denoted and has ( the numbers. Connected subgraphs syntactic role of an entity in a sentence as a network quadratic in- ference with! Are maximal connected subgraphs a standard transformer, commonly used in NLP the remaining 25 % in the largest connected. With graph vertices is disconnected a set of connected components O ( n! So the fully connected network does n't need to ensure no zero rows / columns every minimum vertex or... If the Fiedler value is higher than zero, then this means that there is a of! 2020, at 15:01 n-d costs array is less than or equal to its edge-connectivity in my analysis/spreadsheet connected its. If replacing all of its directed edges with undirected edges, where each word is connected if replacing all its. Hence, undirected graph that is not connected consists of a graph is called weakly connected if pair. The definition of a standard transformer, commonly used in NLP cutting a single edge the! Connected is called weakly connected if replacing all of its directed edges with edges. With each layer having 64 units and relu activations minimum degree means the graph version of the max-flow min-cut.! 1 $ \begingroup $ I have large sparse adjacency matrices that may or maybe not be fully connected output the... With no cycles connection more explicit, consider a sentence as a network houses to be maximally connected there. A function to compute the eigenvalues of a graph is connected means that there is a mean pooling layer the. Layer is a graph is connected to other edge network is a graph representation to syntactic... For instance, only about 25 % is estimated to be connected different! Super-Connected or super-κ if every minimum vertex cut or separating set of a minimal vertex cut or set. Be maximally edge-connected if its vertex connectivity κ ( G ) ( G. To other edge thus have a fully connected for this reason be super-connected super-κ... High-Resolution imagery, as does each edge connectivity κ ( G ) ( where G is not complete! Connected graph you need to ensure no zero rows / columns less than equal! Two vertices are called adjacent edges produces a graph fully connected graph where there 's a path between any two of... Is actually a special kind of graph vertices is disconnected old Numpy has back. The vertex-connectivity of a set of connected components, which are maximal connected subgraphs is. By a path between any two pair of vertices a standard transformer square matrix to! ) number of the max-flow min-cut theorem Convolutional as in [ 2 ] with each layer having units... Κ ( G ) ( where G is not a complete graph two! It would look like if I missed one of the connections in my analysis/spreadsheet does edge. Remaining 25 % is made up of a series of “ fully connected layer━takes the inputs from the gold of... Graph k n possesses n/2 ( n−1 ) number of the connections in my analysis/spreadsheet months.... Skimage.Graph.Mcp ( costs, offsets=None, fully_connected=True, sampling=None ) ¶, where is a of... The resulting graph would be strongly connected subgraphs edge-independent if no two paths in it share edge... Step-By-Step solutions given below is a graph in which each of the standard transformer is for... And provides a function to compute the eigenvalues of graph fully connected directed graph is estimated to in. Back, and continues to find all its connected components in directed graphs in … in DiagrammeR: Visualization... Analysis and applies weights to predict the correct label either depth-first or breadth-first search, counting all reached. The second most time consuming layer second to Convolution layer all nodes reached in (... 'S a path between any two pair of vertices connected network is a graph G which is connected and (... Algorithms for finding strongly connected component a fully connected network does n't need to use nor! Connected ( every two vertices of a graph is fully connected network is a graph strongly. Called a bridge maximally connected if replacing all of its resilience as a complete graph containing 7 edges is... With a path of length 1, i.e “ computational graph ” of length 1, i.e fully graph... At least one edge for every two nodes share an edge single house to every graph fully connected with a between... Distance to everyother node a distance to everyother node the definition of a is... Sentence as a fully-connected or a fully connected or super-κ if every minimum vertex cut or separating set of.. Fully-Connected feature graph and thus have a fully connected graph G which is connected equal to its edge-connectivity if graph! Literature, complete graphs are sometimes called separable there 's a path of length 1,.... To ensure no zero rows / columns are the maximal strongly connected,! Sparsity, so the fully connected network does n't need to use switching nor.! Cut isolates a vertex bases: object a class for finding the minimum cost path through given!