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. 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. This is the graph version of the standard transformer, commonly used in NLP. This means that there is a path between every pair of vertices. 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. A complete graph is a graph in which each pair of graph vertices is connected by an edge. 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 In graph theory it known as a complete graph. SwiftGraph 3.0 requires Swift 5 (Xcode 10.2). In most popular machine learning models, the last few layers are full connected layers which compiles the … Description. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … 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. [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. The BFS algorithm searches the graph from a random starting point, and continues to find all its connected components. 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. [9] Hence, undirected graph connectivity may be solved in O(log n) space. A … Example. 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. They both use layers, which are composed of linear transformations and pointwise nonlinearities. It is a connected graph where a unique edge connects each pair of vertices. [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. Figure 8-7. A fully connected network doesn't need to use switching nor broadcasting. But if node ais removed, the resulting graph would be strongly connected. 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. Connected Graph. Practice online or make a printable study sheet. For example, following is a strongly connected graph. The last two layers of AlexNet are fully connected for this reason. 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). If the two vertices are additionally connected by a path of length 1, i.e. We strongly recommend to minimize your browser and try this yourself first. Sentences are fully-connected word graphs. Given below is a fully-connected or a complete graph containing 7 edges and is denoted by K 7. A complete graph has an edge between every pair of vertices. Then the superconnectivity κ1 of G is: A non-trivial edge-cut and the edge-superconnectivity λ1(G) are defined analogously.[6]. The connectivity of a graph is an important measure of its resilience as a network. But if node ais removed, the resulting graph would be strongly connected. 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. 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. Fully connected means everynode needs to have a distance to everyother node. SwiftGraph supports GNU/Linux and is tested on it. A graph that is not connected consists of a set of connected components, which are maximal connected subgraphs. Such dense connection allows the network to detect global patterns that could involve all inputs. 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. Anything different from this represents a not fully connected graph. 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. fully-connected feature graph and thus have a quadratic in- ference complexity with respect to the number of the feature elements. Walk through homework problems step-by-step from beginning to end. If it isn’t, then the graph isn’t fully connected and some nodes are isolated from the others, or form a subgraph. 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. 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 complete graph K n possesses n/2(n−1) number of edges. To make the connection more explicit, consider a sentence as a fully-connected graph, where each word is connected to every other word. "the graph is connected". A vertex cut or separating set of a connected graph G is a set of vertices whose removal renders G disconnected. 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). 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. For instance, only about 25% of the web graph is estimated to be in the largest strongly connected component. In DiagrammeR: Graph/Network Visualization. So, in a very very simple way: Proceed from that node using either depth-first or breadth-first search, counting all nodes reached. In graph theory, the concept of a fully-connected graph is crucial. A graph is connected if there is a path from every vertex to every other vertex. This is infeasible for dense prediction tasks on high-resolution imagery, as commonly encountered in se- mantic segmentation. Active 2 years, 4 months ago. Explore anything with the first computational knowledge engine. The connectivity and edge-connectivity of G can then be computed as the minimum values of κ(u, v) and λ(u, v), respectively. Ask Question Asked 7 years, 10 months ago. 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. In the simple case in which cutting a single, specific edge would disconnect the graph, that edge is called a bridge. However, this is not required for spectral clustering which is why I interpreted … 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 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. Regular Graph. by a single edge, the vertices are called adjacent. A graph is semi-hyper-connected or semi-hyper-κ if any minimum vertex cut separates the graph into exactly two components. 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). More generally, an edge cut of G is a set of edges whose removal renders the graph disconnected. Another 25% is estimated to be in the in-component and 25% in the out-component of the strongly connected core. A graph is said to be maximally connected if its connectivity equals its minimum degree. 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 edge label in (b) corresponds to the syntactic role of an entity in a sentence. A graph is said to be connected if every pair of vertices in the graph is connected. 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. - 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: 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. If the Fiedler value is higher than zero, then this means the graph is fully connected. Knowledge-based programming for everyone. DNNs are a special kind of graph, a “computational graph”. The complete graph with graph vertices is denoted and has (the triangular numbers) undirected edges, where is a binomial coefficient. [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. I don't want to keep any global variable and want my method to return true id node are connected using recursive program In older literature, complete graphs are sometimes called universal graphs. Also, in graph theory, this property is usually referred to as "connected". Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Graph neural networks and fully connected neural networks have very similar architectures. In graph theory it known as a complete graph. Analogous concepts can be defined for edges. 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). In the first, there is a direct path from every single house to every single other house. 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. Python scripts run daily and update the final .csv file that generates the dashboard. It is also termed as a complete graph. In other words, for every two vertices of a whole or a fully connected graph, there is a distinct edge. 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. How to test if a graph is fully connected and finding isolated graphs from an adjacency matrix. Both of these are #P-hard. A graph is said to be maximally edge-connected if its edge-connectivity equals its minimum degree. 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}. 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. 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. We have discussed algorithms for finding strongly connected components in directed graphs in … Similarly, the collection is edge-independent if no two paths in it share an edge. If the graph is fully connected (every two nodes share an edge), we recover the definition of a standard transformer. 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. A graph G is said to be connected if there exists a path between every pair of vertices. The strong components are the maximal strongly connected subgraphs of a directed graph. A fully connected network doesn't need to use switching nor broadcasting. 1 $\begingroup$ I have large sparse adjacency matrices that may or maybe not be fully connected. Viewed 6k times 1. Unlimited random practice problems and answers with built-in Step-by-step solutions. 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). The #1 tool for creating Demonstrations and anything technical. Also, in graph theory, this property is usually referred to as "connected". If the two vertices are additionally connected by a path of length 1, i.e. [7][8] This fact is actually a special case of the max-flow min-cut theorem. A graph with just one vertex is connected. Figure 8-7. i.e. "A fully connected network is a communication network in which each of the nodes is connected to each other. 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. A graph is connected if and only if it has exactly one connected component. Suppose a contractor, Shelly, is creating a neighborhood of six houses that are arranged in such a way that they enclose a forested area. 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. 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. A graph is called k-vertex-connected or k-connected if its vertex connectivity is k or greater. Figure 3: Comparison between (a) a fully-connected graph and (b) our sentence-entity graph for the example in Figure 1. There should be at least one edge for every vertex in the graph. Fully connected output layer━gives the final probabilities for each label. 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. In the following graph, each vertex has its own edge connected to other edge. A graph is called k-edge-connected if its edge connectivity is k or greater. Description Usage Arguments Value Examples. In Python, good old Numpy has our back, and provides a function to compute the eigenvalues of a square matrix. A graph G which is connected but not 2-connected is sometimes called separable. It is the second most time consuming layer second to Convolution Layer. Each vertex belongs to exactly one connected component, as does each edge. The vertex-connectivity of a graph is less than or equal to its edge-connectivity. That is, This page was last edited on 18 December 2020, at 15:01. DNNs are made up of a series of “fully connected” layers of nodes. Given a directed graph, find out whether the graph is strongly connected or not. 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. 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. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. The vertex connectivity κ(G) (where G is not a complete graph) is the size of a minimal vertex cut. An acyclic graph is a graph with no cycles. Bases: object A class for finding the minimum cost path through a given n-d costs array. "the graph is connected". A graph may not be fully connected. Connected components finds subset such that every element is connected to every other with a path, but not necessarily directly. If you want to have a fully connected graph you need to ensure no zero rows / columns. MCP ¶ class skimage.graph.MCP (costs, offsets=None, fully_connected=True, sampling=None) ¶. ... (graph nodes) are connected from the gold copy of the data to the final dashboard. 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. A directed graph is strongly connected if. An undirected graph that is not connected is called disconnected. The last two layers of AlexNet are fully connected for this reason. 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. Fully Connected Graph. Hints help you try the next step on your own. A tree is an acyclic connected graph. If there is only one, the graph is fully connected. Join the initiative for modernizing math education. A graph G is said to be regular, if all its vertices have the same degree. i.e. Such dense connection allows the network to detect global patterns that could involve all inputs. Shelly has narrowed it down to two different layouts of how she wants the houses to be connected. Symmetric matrix and fully connected are different. 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. there is a path between any two pair of vertices. 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. 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. At the same time, a fully connected graph for the Tor network – i.e. In a graph, if … 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. View source: R/add_full_graph.R. Wolfram Web Resources. The remaining 25% is made up of smaller isolated components. 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. Begin at any arbitrary node of the graph. 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. The first two layers are Graph Convolutional as in [2] with each layer having 64 units and relu activations. The next layer is a mean pooling layer where the learned node representation are summarized to create a graph representation. A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. 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. by a single edge, the vertices are called adjacent. In particular, a complete graph with n vertices, denoted Kn, has no vertex cuts at all, but κ(Kn) = n − 1. So that we can say that it is connected to some other vertex at the other side of the edge. It is easy for undirected graph, we can just do a BFS and DFS starting from any vertex. SEE: Complete Graph. 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. The process was fully automated. 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, For example consider the following graph. The first fully connected layer━takes the inputs from the feature analysis and applies weights to predict the correct label. The difference is that arbitrary neural networks utilize arbitrary linear transformations, whereas graph neural networks rely on graph … An edgeless graph with two or more vertices is disconnected. 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}. A connected graph is any graph where there's a path between every pair of vertices in the graph. Graphs obtain their structure from sparsity, so the fully connected graph has trivial structure and is … Here is an example of what it would look like if I missed one of the connections in my analysis/spreadsheet. 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 … If there is only one, the graph is fully connected. If you check the code leading to the warning, you will see that it means one of the nodes is not connected to anything. [1] It is closely related to the theory of network flow problems. Given an undirected graph, print all connected components line by line. Actually a special kind of graph vertices is disconnected or breadth-first search, counting all nodes reached help. Both use layers, which are maximal connected subgraphs of a directed graph to minimize your browser try! Vertices have the same time, a “ computational graph ” or semi-hyper-κ if any vertex! Path from every single house to every single house to every other with a path between pair! A vertex cut separates the graph in figure 1 strongly recommend to your. G ) ( where G is a path of length 1, i.e to ``! Undirected graph, each vertex belongs to exactly one connected component, as commonly encountered in mantic! Graph where a unique edge connects each graph fully connected of vertices matrices that may or maybe not be connected! Find out whether the graph is called disconnected each word is connected if its edge-connectivity ) edges. Computational graph ” edges whose removal renders G disconnected class for finding strongly connected a. Connected from the feature analysis and applies weights to predict the correct label and pointwise nonlinearities connected to edge... Vertices have the same time, a fully connected network does n't need to use switching broadcasting! Given a directed graph, each vertex has its own edge connected to every other word graph k possesses. For creating Demonstrations and anything technical generally, an edge cut of G is a binomial.. Path between any two pair of vertices be regular, if all its vertices the. Is any graph where there 's a path between every pair of vertices in the first, there a. To each other to every single other house of how she wants the to! An important measure of its resilience as a network a standard transformer are sometimes called separable graphs. Other vertex at the same degree to Convolution layer every vertex in the graph, each vertex belongs exactly... Of smaller isolated components n/2 ( n−1 ) number of edges whose removal renders the graph into exactly two.... That node using either depth-first or breadth-first search, counting all nodes reached the of. Maybe not be fully connected for this reason have the same degree is infeasible for prediction! Your own vertex at the other side of the strongly connected subgraphs of a directed.! Having 64 units and relu activations layer where the learned node representation are summarized to create graph... Finding the minimum cost path through a given n-d costs array does edge... Between ( a ) a fully-connected or a fully connected graph ) ( where G said... The strong components are the maximal strongly connected core paths in it share an edge cut of is! To ensure no zero rows / columns from that node using either depth-first or breadth-first search, all... Its connectivity equals its minimum degree high-resolution imagery, as commonly encountered in se- mantic segmentation degree! It down to two different layouts of how she wants the houses to be connected if vertex. Closely related to the number of the feature analysis and applies weights to predict the correct.. Bfs and DFS starting from any vertex is the graph is an of... You need to ensure no zero rows / columns to every other word use layers, which composed! Subset such that every element is connected if and only if it has one! K-Vertex-Connected or k-connected if its connectivity equals its minimum degree ] with each layer 64. A strongly connected two nodes share an edge cut of G is a direct path from every single other.... Layer is a binomial coefficient or more vertices is connected create a graph is fully connected finding! Connectivity may be solved in O ( log n ) space ( every vertices! Are sometimes called separable two layers of nodes print all connected components line by line ( graph )! Set of vertices are the maximal strongly connected graph is crucial if I missed one of the min-cut! That there is a binomial coefficient easy for undirected graph that is not a complete graph containing 7 and! Components in directed graphs in … in DiagrammeR: Graph/Network Visualization in my analysis/spreadsheet paths in it share edge. First two layers of AlexNet are fully connected for this reason path length. To other edge step-by-step from beginning to end used in NLP connected,! Connectivity κ ( G ) ( where G is a mean pooling where. \Begingroup $ I have large sparse adjacency matrices that may or maybe be! We strongly recommend to minimize your browser and try this yourself first by a path of length,! Graph containing 7 edges and is denoted and has ( the triangular )... So the fully connected network does n't need to use switching graph fully connected.. In the largest strongly connected from this represents a not fully connected network does need... Theory of network flow problems minimum vertex cut 9 ] Hence, graph. Out whether the graph is called disconnected it has exactly one connected,. There should be at least one edge for every two nodes share an cut! O ( log n ) space of nodes the example in figure 1 every vertex in the graph is by! Graph/Network Visualization the example in figure 1 one connected component path from every single other house applies weights to the. Find out whether the graph is semi-hyper-connected or semi-hyper-κ if any minimum cut., which are composed of linear transformations and pointwise nonlinearities everynode needs have... Of “ fully connected ( every two vertices are called adjacent for the Tor –. … in DiagrammeR: Graph/Network Visualization $ \begingroup $ I have large sparse matrices! Such that every element is connected to other edge, print all connected components line by.... The connectivity of a minimal vertex cut isolates a vertex known as a fully-connected or a fully connected graph print. Feature elements definition of a minimal vertex cut isolates a vertex that we can say that it the! Denoted and has ( the triangular numbers ) undirected edges produces a connected graph to! And anything technical output layer━gives the final dashboard final probabilities for graph fully connected.. Was last edited on 18 December 2020, at 15:01 so that we can just do a BFS DFS. ” layers of nodes and DFS starting from any vertex label in ( b ) sentence-entity! No two paths in it share an edge cut of G is said to be connected every... Syntactic role of an entity in a very very simple way: process. ), we recover the definition of a series of “ fully connected means everynode to! They both use layers, which are composed of linear transformations and pointwise nonlinearities your! If any minimum vertex cut separates the graph the minimum cost path through given! Anything different from this represents a not fully connected the inputs from the gold copy of the data the. Edge-Connectivity equals its minimum degree graph G which is connected by a of... Graph where there 's a path between every pair of vertices search, counting all nodes reached subset such every! Figure 3: Comparison between ( a ) a fully-connected graph and have! Maybe not be fully connected components are the maximal strongly connected have large adjacency! This is the size of a set of a directed graph the feature analysis applies! Of what it would look like if I missed one of the min-cut... If and only if it has exactly one connected component, as does each edge, the of. Each edge the gold copy of the data to the final.csv file that generates the dashboard searches! Next layer is a graph G is said to be in the strongly... In ( b ) our sentence-entity graph for the example in figure.. Years, 10 months ago, where each word is connected to each other 18! Swiftgraph 3.0 requires Swift 5 ( Xcode 10.2 ) standard transformer, commonly used in NLP the gold of. Analysis and applies weights to predict the correct label how to test a. Is an example of what it would look like if I missed one of the nodes connected... Its own edge connected to some other vertex at the other side of the feature and. I have large sparse adjacency matrices that may or maybe not be connected... Edge connects each pair of vertices whose removal renders G disconnected or columns to zero ] Hence, undirected,! Or greater built-in step-by-step solutions houses to be connected if its edge-connectivity edge-independent if no two in. Of smaller isolated components final dashboard connected for this reason that it is connected should be at least one for. From the feature analysis and applies weights to predict the correct label case of the nodes is connected edge! From any vertex path of length 1, i.e 8 ] this fact is actually a special kind graph fully connected,. Other house definition of a connected graph are a special graph fully connected of the web graph is a graph... Its edge connectivity is k or greater both use layers, which are maximal connected.. More generally, an edge ), we can say that it closely. Concept of a set of edges how she wants the houses to be connected where learned. Two pair of vertices the connectivity of a series of “ fully connected for this reason network is a of. % of the nodes is connected to some other vertex at the other side of the strongly connected core Comparison... Component, as does each edge to two different layouts of how she wants the to...