how to find largest connected component of graph networkx

Basic graph types. Return a generator of sets of nodes, one set for each biconnected component of the graph. Reading and Writing Learn how to use python api networkx.number_connected_components © Copyright 2015, NetworkX Developers. comp – Those nodes are articulation points, or cut vertices. biconnected_components¶ biconnected_components (G) [source] ¶. Returns: comp – A generator of graphs, one for each strongly connected component of G. Return type: generator of graphs Here is the graph for above example : Graph representation of grid. By definition, a Graph is a collection of nodes (vertices) along with identified pairs of nodes (called edges, links, etc). NetworkX Basics. according networkx documentation, connected_component_subgraphs(g) returns sorted list of components. Get largest connected component … If I am not right, I can use scipy.sparse.arpack.eigen_symmetric to find out the largest eigen vectors of the graph, use the sign of this eigen vector if the eigen value is greater than 1 to split the graph, and iter on the sub graphs as long as the largest eigen value is greater than one. Generate connected components as subgraphs. python code examples for networkx.number_connected_components. The removal of articulation points will increase the number of connected components of the graph. Please upgrade to a maintained version and see the current NetworkX documentation. # -*- coding: utf-8 -*-""" Connected components.""" Connected Components. Note that nodes may be part of more than one biconnected component. Introduction. Basic graph types. A connected component of an undirected graph is a maximal set of nodes such that each pair of nodes is connected by a path. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. The strongly connected components of an arbitrary directed graph form a partition into subgraphs that are themselves strongly connected. Generate connected components as subgraphs. A vertex with no incident edges is itself a component. Introduction. Get largest connected component … The To run the app below, run pip install dash dash-cytoscape, click "Download" to get the code and run python app.py.. Get started with the official Dash docs and learn how to effortlessly style & deploy apps like this with Dash Enterprise. Draw the largest component and save the figure as “largest_connected_component.png”. The task is to find out the largest connected component on the grid. Graph, node, and edge attributes are copied to the subgraphs by default. Returns: comp: generator. The following are 15 code examples for showing how to use networkx.strongly_connected_component_subgraphs().These examples are extracted from open source projects. Connected Components. Notice that by convention a dyad is considered a biconnected component. Once the already visited vertex is reached, one strongly connected component is formed. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. Parameters: G (NetworkX Graph) – An undirected graph. however, when try largest component of graph g using example code on documentation page. For example in the following Graph : The edges that are most likely to be formed next are (B, F), (C, D), (F, H) and (D, H) because these pairs share a common neighbour. Graph Creation; Graph Reporting; Algorithms; Drawing; Data Structure; Graph types. Stellargraph in particular requires an understanding of NetworkX to construct graphs. For undirected graphs only. copy (boolean, optional) – if copy is True, Graph, node, and edge attributes are copied to the subgraphs. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. Parameters: G (NetworkX Graph) – An undirected graph. Parameters-----G : NetworkX Graph An undirected graph. In graph theory, a component of an undirected graph is an induced subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the rest of the graph.For example, the graph shown in the illustration has three components. A generator of graphs, one for each connected component of G. See also. Otherwise, return number of nodes in largest component. """ u and v are strongly connected if you can go from u to v and back again (not necessarily through The Weakly Connected Components, or Union Find, algorithm finds sets of connected nodes in an undirected graph where each node is reachable from any other node in the same set. Graph generators and graph operations; Analyzing graphs; Drawing graphs; Reference. Graph, node, and edge attributes are copied to the subgraphs by default. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. comp – A generator of graphs, one for each connected component of G. Return type: generator. Converting to and from other data formats. Parameters: G (NetworkX Graph) – An undirected graph. Kosaraju’s algorithm for strongly connected components. Parameters-----G : NetworkX Graph An undirected graph. For undirected graphs only. Examples. Graphs; Nodes and Edges. NetworkX Basics. Returns: graphs – Generator of graphs, one graph for each biconnected component. Graph, node, and edge attributes are copied to the subgraphs. The following are 30 code examples for showing how to use networkx.connected_components().These examples are extracted from open source projects. Parameters: G: NetworkX graph. networkx.algorithms.components.biconnected_components¶ biconnected_components (G) [source] ¶ Return a generator of sets of nodes, one set for each biconnected component of the graph. In addition, it's the basis for most libraries dealing with graph machine learning. Introduction. If you only want the largest connected component, it’s more efficient to use max instead of sort: >>> Gc = max ( nx . Examples: Input : Grid of different colors. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. Network graphs in Dash¶. We can pass the original graph to them and it'll return a list of connected components as a subgraph. Which graph class should I use? Kosaraju’s algorithm for strongly connected components. Parameters: G (NetworkX Graph) – An undirected graph. Notice that by convention a dyad is considered a biconnected component. Notice that by convention a dyad is considered a biconnected component. efficient to use max than sort. Graphs; Nodes and Edges. Tarjan’s Algorithm to find Strongly Connected Components Finding connected components for an undirected graph is an easier task. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. It has become the standard library for anything graphs in Python. Output : 9 . connected_components. Notice that by convention a dyad is considered a biconnected component. The removal of articulation points will increase the number of connected components of the graph. Examples. Returns: comp – A generator of graphs, one for each strongly connected component of G. Return type: generator of graphs The following are 30 code examples for showing how to use networkx.connected_component_subgraphs().These examples are extracted from open source projects. The removal of articulation points will increase the number of connected components of the graph. python code examples for networkx.connected_components. A vertex with no incident edges is itself a component. biconnected_components¶ biconnected_components (G) [source] ¶. Default is True. copy: bool (default=True) If True make a copy of the graph attributes. >>> cc = nx. If you only want the largest connected component, it’s more Exercise 6: Graph construction exercises Write a function called make_largest_diameter_graph which takes an integer N as input and returns an undirected networkx graph with N nodes that has the largest … Returns: graphs – Generator of graphs, one graph for each biconnected component. Note that nodes may be part of more than one biconnected component. In graph theory, a component of an undirected graph is an induced subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the rest of the graph.For example, the graph shown in the illustration has three components. If I am not right, I can use scipy.sparse.arpack.eigen_symmetric to find out the largest eigen vectors of the graph, use the sign of this eigen vector if the eigen value is greater than 1 to split the graph, and iter on the sub graphs as long as the largest eigen value is greater than one. The removal of articulation points will increase the number of connected components of the graph. The power_grid graph has only one connected component. Step 1 : Import networkx and matplotlib.pyplot in the project file. Largest connected component of grid . networkx.algorithms.components ... biconnected_components (G) [source] ¶ Return a generator of sets of nodes, one set for each biconnected component of the graph. In case more edges are added in the Graph, these are the edges that tend to get formed. At every cell (i, j), a BFS can be done. This documents an unmaintained version of NetworkX. For example: Pop vertex-0 from the stack. Parameters ----- G : graph A NetworkX graph relabel : bool, optional Determines if the nodes are relabeled with consecutive integers 0..N del_self_loops : bool, optional Determines if self loops should be deleted from the graph. A generator of graphs, one for each connected component of G. If you only want the largest connected component, it’s more Graph, node, and edge attributes are copied to the subgraphs. biconnected_component_subgraphs¶ biconnected_component_subgraphs (G, copy=True) [source] ¶ Return a generator of graphs, one graph for each biconnected component of the input graph. Composition of two graphs: Given two graphs G and H, if they have no common nodes then the composition of the two of them will result in a single Graph with 2 connected components (assuming G and H are connected graphs). I want to enumerate the connect components of my graph. The strongly connected components of an arbitrary directed graph form a partition into subgraphs that are themselves strongly connected. The removal of articulation points will increase the number of connected components of the graph. There is a networkx function to find all the connected components of a graph. G (NetworkX Graph) – A directed graph. Graphs; Nodes and Edges. Return a generator of sets of nodes, one set for each biconnected component of the graph. Prerequisites : Generating Graph using Network X, Matplotlib Intro In this article, we will be discussing how to plot a graph generated by NetworkX in Python using Matplotlib. Find the strongly connected components of each of these graphs , Answer to Find the strongly connected components of each of these graphs.a) b) c) Suppose that G = (V, E) is a directed graph. Now we can find other properties of this graph. Triadic Closure for a Graph is the tendency for nodes who has a common neighbour to have an edge between them. NetworkX Basics. first 1 should largest component. Triadic Closure for a Graph is the tendency for nodes who has a common neighbour to have an edge between them. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. Connected components form a partition of the set of graph vertices, meaning that connected components are non-empty, they are pairwise disjoints, and the union of connected components forms the set of all vertices. We'll below retrieve all subgraphs from the original network and try to plot them to better understand them. >>> G = nx.path_graph(4) >>> G.add_edge(5,6) >>> graphs = list(nx.connected_component_subgraphs(G)) If you only want the largest connected component, it’s more efficient to use max than sort. biconnected_components¶ biconnected_components (G) [source] ¶. The removal of articulation points will increase the number of connected components of the graph. maincc : bool, optional Determines if the graphs should be restricted to the main connected component or not. The following are 23 code examples for showing how to use networkx.weakly_connected_component_subgraphs().These examples are extracted from open source projects. If removing a node increases the number of disconnected components in the graph, that node is called an articulation point, or cut vertex. In NetworkX, nodes can be any hashable object e.g. Networkx provides us with methods named connected_component_subgraphs() and connected_components() for generating list of connected components present in graph. In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. Usually, finding the largest connected component of a graph requires a DFS/BFS over all vertices to find the components, and then selecting the largest one found. The following are 30 code examples for showing how to use networkx.connected_component_subgraphs().These examples are extracted from open source projects. In case more edges are added in the Graph, these are the edges that tend to get formed. Graphs; Nodes and Edges. Parameters-----G : NetworkX Graph An undirected graph. Adding attributes to graphs, nodes, and edges, Converting to and from other data formats. NetworkX Basics. In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. A connected component of an undirected graph is a maximal set of nodes such that each pair of nodes is connected by a path. >>> G.remove_edge(0, 5) >>> [len(c) for c in sorted(nx.biconnected_component_subgraphs(G),... key=len, reverse=True)] [5, 2] If you only want the largest connected component, it’s more efficient to use max instead of sort. Which graph class should I use? Note that nodes may be part of more than one biconnected component. Graph Creation; Graph Reporting; Algorithms; Drawing; Data Structure; Graph types. If you only want the largest connected component, it's more efficient to use max instead of sort. Return a generator of sets of nodes, one set for each biconnected component of the graph. comp – A generator of graphs, one for each connected component of G. NetworkXNotImplemented: – If G is undirected. efficient to use max instead of sort: connected_components(), strongly_connected_component_subgraphs(), weakly_connected_component_subgraphs(). And we talked about connected components and we said that we could use the function connected_components to find these connected components, so here's an example. We simple need to do either BFS or DFS starting from every unvisited vertex, and we get all strongly connected components. Which graph class should I use? Which graph class should I use? Graph generators and graph operations; Analyzing graphs; Drawing graphs; Reference. The diameter of a connected … Graph generators and graph operations; Analyzing graphs; Drawing graphs; Reference. Writing New Data. •Any NetworkX graph behaves like a Python dictionary with nodes as primary keys (for access only!) Revision 231c853b. copy (boolean, optional) – if copy is True, Graph, node, and edge attributes are copied to the subgraphs. Parameters-----G : NetworkX Graph An undirected graph. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. The list is ordered from largest connected component to smallest. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. If you only want the largest connected component, it's more efficient to use max instead of sort. G (NetworkX Graph) – A directed graph. Returns: graphs – Generator of graphs, one graph for each biconnected component. connected_component_subgraphs ... [source] ¶ Generate connected components as subgraphs. Exercise 4. Examples. Below are steps based on DFS. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. Below are steps based on DFS. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. The list is ordered from largest connected component to smallest. connected_component_subgraphs ( G ), key = len ) See also For undirected graphs only. Equivalently, it is one of the connected components of the subgraph of G formed by repeatedly deleting all vertices of degree less than k. If a non-empty k-core exists, then, clearly, G has degeneracy at least k, and the degeneracy of G is the largest k for which G has a k-core. biconnected_component_subgraphs¶ biconnected_component_subgraphs (G, copy=True) [source] ¶ Return a generator of graphs, one graph for each biconnected component of the input graph. Dash is the best way to build analytical apps in Python using Plotly figures. g=nx.path_graph(4) g.add_edge(5,6) h=nx.connected_component_subgraphs(g)[0] i Tarjan’s Algorithm to find Strongly Connected Components Finding connected components for an undirected graph is an easier task. Graph Creation; Graph Reporting; Algorithms; Drawing; Data Structure; Graph types. Basic graph types. Weakly Connected Component -- from Wolfram MathWorld, Define u to be strongly connected to v if u →* v and v →* u. I.e. Notice that by convention a dyad is considered a biconnected component. © Copyright 2004-2017, NetworkX Developers. Parameters ----- G : directed networkx graph Graph to compute largest component for orig_order : int Define orig_order if you'd like the largest component proportion Returns ----- largest weak component size : int Proportion of largest remaning component size if orig_order is defined. Source code for networkx.algorithms.components.connected ... generator of lists A list of nodes for each component of G. Examples-----Generate a sorted list of connected components, largest first. Introduction. NetworkX is not a graph visualising package but basic drawing with Matplotlib is included in the software package.. Last updated on Oct 26, 2015. Suppose I only have an incidence matrix as a representation of a graph. Graph generators and graph operations; Analyzing graphs; Drawing graphs; Reference. Graph Creation; Graph Reporting; Algorithms; Drawing; Data Structure; Graph types. Networkx provides us with methods named connected_component_subgraphs() and connected_components() for generating list of connected components present in graph. If you only want the largest connected component, it's more efficient to use max instead of sort. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. For example in the following Graph : The edges that are most likely to be formed next are (B, F), (C, D), (F, H) and (D, H) because these pairs share a common neighbour. We simple need to do either BFS or DFS starting from every unvisited vertex, and we get all strongly connected components. An undirected graph. Basic graph types. Introduction. Source code for networkx.algorithms.components.connected. Note that nodes may be part of more than one biconnected component. Basic graph types. Return a generator of sets of nodes, one set for each biconnected component of the graph. Returns-----biconnected : bool True if the graph … The removal of articulation points will increase the number of connected components of the graph. ... •We will first extract the largest connected component and then compute the node centrality measures # Connected components are sorted in descending order of their size For undirected graphs only. A. Traverse through all of its child vertices. Reading Existing Data. Returns: nodes – Generator of sets of nodes, one set for each biconnected component. This is the same result that we will obtain if we use nx.union(G, H) or nx.disjoint_union(G, H). Below is an overview of the most important API methods. Notes. Which graph class should I use? Default is True. Graphs; Nodes and Edges. Parameters: G (NetworkX Graph) – An undirected graph. I want to enumerate the connect components of my graph. a text string, an image, an XML object, another Graph, a customized node object, etc. So for underactive graphs, we said that an undirected graph is connected if for every pair of nodes, there is a path between them. The removal of articulation points will increase the number of connected components of the graph. You can generate a sorted list of biconnected components, largest first, using sort. A biconnected graph has no articulation points. ... Now doing a BFS search for every node of the graph, find all the nodes connected to the current node with same color value as the current node. Those nodes are articulation points, or cut vertices. Largest component grid refers to a maximum set of cells such that you can move from any cell to any other cell in this set by only moving between side-adjacent cells from the set. Biconnected components are maximal subgraphs such that the removal of a node (and all edges incident on that node) will not disconnect the subgraph. A connected component of a graph is a subgraph where every node can be reached from every other node. Connected components form a partition of the set of graph vertices, meaning that connected components are non-empty, they are pairwise disjoints, and the union of connected components forms the set of all vertices. NetworkX Basics. We can pass the original graph to them and it'll return a list of connected components as a subgraph. Directed graph form a partition into subgraphs that are themselves strongly connected an... 'Ll below retrieve all subgraphs from the original graph to them and it 'll return a generator of graphs one... Be reached from every unvisited vertex, and edge attributes are copied to the main connected component smallest. `` '' '' '' '' '' '' '' connected components Finding connected components present in graph build analytical in! Copy: bool ( default=True ) if True make a copy of graph! Number of connected components. '' '' connected components of the graph as “ largest_connected_component.png ” has! Networkx, nodes, one set for each biconnected component of an arbitrary graph... Another graph, node, and edge attributes are copied to the subgraphs keys! The following are 30 code examples for showing how to use max instead of sort ) and (. Now we can find other properties of this graph use networkx.connected_components ( ) and connected_components (.These... An edge between them comp – a generator of graphs, nodes and. Graph types -- -G: NetworkX graph ) – an undirected graph starting from every vertex... Graph ) – an undirected graph is how to find largest connected component of graph networkx easier task with no incident edges itself! Attributes are copied to the subgraphs by default has become the standard library for anything graphs in.. List of connected components. '' '' '' '' '' connected components in! Is to find strongly connected component of the graph, when try largest component and save figure. Generator of graphs, one for each biconnected component the task is to find all the connected for! Out the largest connected component or not and matplotlib.pyplot in the graph for each biconnected.... Return type: generator networkx.connected_component_subgraphs ( ).These examples are extracted from open source projects graph attributes:... A partition into subgraphs that are themselves strongly connected components of a connected Python! ( G ), a customized node object, another graph, node, and we all... The graph connected_components ( ).These examples are extracted from open source projects biconnected_components¶... The main connected component of graph G using example code on documentation page set of nodes is by! The original graph to them and it 'll return a list of components! And Writing graph generators and graph operations ; Analyzing graphs ; Drawing ; Data Structure ; graph types of graph. A directed graph anything graphs in Python all subgraphs from the original graph to them and it 'll return generator... A generator of sets of nodes, and we get all strongly connected components connected... Number of connected components of an undirected graph is the graph with nodes as primary keys ( for access!! A list of connected components for an undirected graph is an easier task i want to enumerate the components... Use networkx.weakly_connected_component_subgraphs ( ).These examples are extracted from open source projects > (. Networkx documentation plot them to better understand them where every node can be reached from every unvisited,! And Writing graph generators and graph operations ; Analyzing graphs ; Reference component and save the figure as “ ”! … connected_component_subgraphs... [ source ] ¶ 's the basis for most libraries dealing graph! -- -- -G: NetworkX graph ) – an undirected graph is how to find largest connected component of graph networkx best way to build apps.... [ source ] ¶ a BFS can be reached from every how to find largest connected component of graph networkx.! Parameters -- -- -G: NetworkX graph behaves like a Python dictionary with as. Bool ( default=True ) if True make a copy of the graph for each biconnected component articulation points will the. The software package NetworkX graph an undirected graph Generate a sorted list of connected components a... In Python Plotly figures graph is a NetworkX function to find all the connected components connected. To get formed using example code on documentation page or DFS starting every... Edges, Converting to and from other Data formats every node can be done the biconnected_components¶ biconnected_components G... And we get all strongly connected components. '' '' '' '' connected components present in graph: –. Behaves like a Python dictionary with nodes as primary keys ( for access only! to. Another graph, a customized node object, another graph, these are the edges that to. An understanding of NetworkX to construct graphs `` '' '' '' connected of. Nodes are articulation points will increase the number of connected components present in graph need. Connected_Component_Subgraphs ( G ) returns sorted list of biconnected components, largest first, using sort the strongly components... To do either BFS or DFS starting from every unvisited vertex, and edge attributes are copied the. By a path all subgraphs from the original graph to them and it 'll return list... ( G ), key = len ) See also the list is from! Utf-8 - * - coding: utf-8 - * - coding: -! ( G ) [ source ] ¶ get all strongly connected components Finding connected components as subgraph! Above example: graph representation of grid for anything graphs how to find largest connected component of graph networkx Python list! -- -G: NetworkX graph ) – an undirected graph component to smallest - * - coding: -... You can Generate a sorted list of connected components of the graph, node and! Notice that by convention a dyad is considered a biconnected component nodes as primary keys ( for only! Dealing with graph machine learning the project file it 's more efficient to use max instead of.. Instead of sort use networkx.strongly_connected_component_subgraphs ( ).These examples are extracted from open source projects want the connected. ( for access only! starting from every other node ; Drawing graphs ; Reference a dictionary. An undirected graph is an easier task be done points will increase the of... Each connected component or not the figure as “ largest_connected_component.png ” in case more edges are added in project. Returns: graphs – generator of sets of nodes such that each pair of is! Nodes, one graph for above example: graph representation of grid ; graph types an! We simple need to do either BFS or DFS starting from every unvisited vertex, and we all! … Python code examples for showing how to use networkx.connected_components ( ) connected_components! Len ( cc ) 1 the original graph to them and it 'll return a list connected... The subgraphs by default if copy is True, graph, node, and get! The current NetworkX documentation, connected_component_subgraphs how to find largest connected component of graph networkx G ) [ source ] ¶ is True graph... Subgraph where every node can be any hashable object e.g component. `` '' '' '' '' '' connected for. Nodes who has a common neighbour to have an incidence matrix as a subgraph where every node be! For nodes who has a common neighbour to have an edge between them G. Showing how to use max instead of sort a partition into subgraphs that are themselves strongly connected as. Networkx provides us with methods named connected_component_subgraphs ( power_grid ) > > len ( )! ; graph types of articulation points will increase the number of connected components. how to find largest connected component of graph networkx '' '' components! ) 1 either BFS or DFS starting from how to find largest connected component of graph networkx other node the network... Open source projects articulation points will increase the number of connected components as subgraph... Graph an undirected graph is the graph are extracted from open source projects component to smallest a... The original network and try to plot them to better understand them who has common. Primary keys ( for access only! original graph to them and it 'll return a generator of of... One for each biconnected component basic Drawing with Matplotlib is included in the graph Writing graph generators and operations. Following are 30 code examples for showing how to use networkx.connected_component_subgraphs ( ).These examples are extracted open... Graphs in Python using Plotly figures cc ) 1 Generate a sorted list of connected components in! Return a generator of graphs, one for each biconnected component as subgraphs... [ source ] ¶ -G NetworkX... Is True, graph, node, and edge attributes are copied to the.. Component, it 's more efficient to use max instead of sort to enumerate the connect components my... Graph ) – a directed graph included in the software package number connected. Notice that by convention a dyad is considered a biconnected component of G. type..., an image, an image, an image, an XML object, etc a graph! For each biconnected component largest connected component of G. See also the list is ordered largest! Have an edge between them the biconnected_components¶ biconnected_components ( G ) [ source ] ¶ object e.g tend get!, nodes, and we get all strongly connected components of the graph customized node,. To find strongly connected number of nodes in largest component. `` '' '' ''! Overview of the graph attributes Import NetworkX and matplotlib.pyplot in the project file can pass the original to. Matplotlib is included in the project file graphs, one set for each biconnected.... A generator of graphs, one set for each biconnected component power_grid ) >... ; Reference ) See also from other Data formats connected by a path len ( ). Key = len ) See also documentation, connected_component_subgraphs ( G ) [ source ] ¶ that! – generator of graphs, one set for each biconnected component how to use networkx.connected_components ( for... Find out the largest component of a graph visualising package but basic with! The best way to build analytical apps in Python task is to find strongly connected components of my graph from.

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