igraph (R interface)

igraph is a fast and open source library for the analysis of graphs or networks. The library consists of a core written in C and bindings for high-level languages including R, Python, and Mathematica. This vignette aims to give you an overview of the functions available in the R interface of igraph. For detailed function by function API documentation, check out https://r.igraph.org/reference/.

NOTE: Throughout this tutorial, we will use words graph and network as synonyms, and also vertex or node as synonyms.


To install the library from CRAN, use:


More details on dependencies, requirements, and troubleshooting on installation are found on the main documentation page.


To use igraph in your R code, you must first load the library:

knitr::opts_chunk$set(fig.width=6, fig.height=6)

Now you have all igraph functions available.

Creating a graph

igraph offers many ways to create a graph. The simplest one is the function make_empty_graph:

g <- make_empty_graph()

The most common way to create a graph is make_graph, which constructs a network based on specified edges. For example, to make a graph with 10 nodes (numbered 1 to 10) and two edges connecting nodes 1-2 and 1-5:

g <- make_graph(edges = c(1,2, 1,5), n=10, directed = FALSE)

Starting from igraph 0.8.0, you can also include literal here, via igraph's formula notation. In this case, the first term of the formula has to start with a "\~" character, just like regular formulae in R. The expressions consist of vertex names and edge operators. An edge operator is a sequence of '-' and '+' characters, the former is for the edges and the latter is used for arrow heads. The edges can be arbitrarily long, ie. you may use as many '-' characters to "draw" them as you like. If all edge operators consist of only '-' characters then the graph will be undirected, whereas a single '+' character implies a directed graph: i.e to create the same graph as above:

g <- make_graph(~ 1--2, 1--5, 3, 4, 5, 6, 7, 8, 9, 10)

We can print the graph to get a summary of its nodes and edges:


This means: Undirected Named graph with 10 vertices and 2 edges, with the exact edges listed out. If the graph has a [name] attribute, it is printed as well.

NOTE: summary does not list the edges, which is convenient for large graphs with millions of edges:


The same function make_graph can create some notable graphs by just specifying their name. For example you can create the graph that represents the social network of Zachary's karate club, that shows the friendship between 34 members of a karate club at a US university in the 1970s:

g <- make_graph('Zachary')

To visualize a graph you can use plot:


A more detailed description of plotting options is provided later on in this tutorial.

Vertex and edge IDs

Vertices and edges have numerical vertex IDs in igraph. Vertex IDs are always consecutive and they start with 1. For a graph with n vertices the vertex IDs are always between 1 and n. If some operation changes the number of vertices in the graphs, e.g. a subgraph is created via induced_subgraph, then the vertices are renumbered to satisfy this criterion.

The same is true for the edges as well: edge IDs are always between 1 and m, the total number of edges in the graph.

NOTE: If you are familiar with the C core or the Python interface of igraph, you might have noticed that in those languages vertex and edge IDs start from 0. In the R interface, both start from 1 instead, to keep consistent with the convention in each language.

In addition to IDs, vertices and edges can be assigned a name and other attributes. That makes it easier to track them whenever the graph is altered. Examples of this pattern are shown later on in this tutorial.

Adding/deleting vertices and edges

Let's continue working with the Karate club graph. To add one or more vertices to an existing graph, use add_vertices:

g <- add_vertices(g, 3)

Similarly, to add edges you can use add_edges:

g <- add_edges(g, edges = c(1,35, 1,36, 34,37))

Edges are added by specifying the source and target vertex IDs for each edge. This call added three edges, one connecting vertices 1 and 35, one connecting vertices 1 and 36, and one connecting vertices 34 and 37.

In addition to the add_vertices and add_edges functions, the plus operator can be used to add vertices or edges to graph. The actual operation that is performed depends on the type of the right hand side argument:

g <- g + edges(c(1,35, 1,36, 34,37))

You can add a single vertex/edge at a time using add_vertex and add_edge.

Warning: If you need to add multiple edges to a graph, it is much more efficient to call add_edges once rather than repeatedly calling add_edge with a single new edge. The same applies when deleting edges and vertices.

If you try to add edges to vertices with invalid IDs (i.e., you try to add an edge to vertex 38 when the graph has only 37 vertices), igraph shows an error:

g <- add_edges(g, edges = c(38,37))

Let us add some more vertices and edges to our graph. In igraph we can use the magrittr package, which provides a mechanism for chaining commands with the operator %\>%:

g <- g %>% add_edges(edges=c(1,34)) %>% add_vertices(3) %>%
     add_edges(edges=c(38,39, 39,40, 40,38, 40,37))

We now have an undirected graph with 40 vertices and 86 edges. Vertex and edge IDs are always contiguous, so if you delete a vertex all subsequent vertices will be renumbered. When a vertex is renumbered, edges are not renumbered, but their source and target vertices will be. Use delete_vertices and delete_edges to perform these operations. For instance, to delete the edge connecting vertices 1-34, get its ID and then delete it:

get.edge.ids(g, c(1,34))
g <- delete_edges(g, 82)

As an example, to create a broken ring:

g <- make_ring(10) %>% delete_edges("10|1")

The example above shows that you can also refer to edges with strings containing the IDs of the source and target vertices, connected by a pipe symbol |. "10|1" in the above example means the edge that connects vertex 10 to vertex 1. Of course you can also use the edge IDs directly, or retrieve them with the get.edge.ids function:

g <- make_ring(5)
g <- delete_edges(g, get.edge.ids(g, c(1,5, 4,5)))

As another example, let's make a chordal graph. Remember that a graph is chordal (or triangulated) if each of its cycles of four or more nodes has a chord, which is an edge joining two nodes that are not adjacent in the cycle. First, let's create the initial graph using graph_from_literal:

g1 <- graph_from_literal(A-B:C:I, B-A:C:D, C-A:B:E:H, D-B:E:F,
                         E-C:D:F:H, F-D:E:G, G-F:H, H-C:E:G:I,

In the example above, the ':' operator was used to define vertex sets. If an edge operator connects two vertex sets, then every vertex from the first set will be connected to every vertex in the second set. Then we use is_chordal to evaluate if our graph is chordal and to search what edges are missing to fill-in the graph:

is_chordal(g1, fillin=TRUE)

We can then add the edges required to make the initial graph chordal in a single line:

chordal_graph <- add_edges(g1, is_chordal(g1, fillin=TRUE)$fillin)

Constructing graphs

In addition to make_empty_graph, make_graph, and make_graph_from_literal, igraph includes many other function to construct a graph. Some are deterministic, i.e. they produce the same graph each single time, e.g. make_tree:

graph1 <- make_tree(127, 2, mode = "undirected")

This generates a regular tree graph with 127 vertices, each vertex having two children. No matter how many times you call make_tree, the generated graph will always be the same if you use the same parameters:

graph2 <- make_tree(127, 2, mode = "undirected")

Other functions generate graphs stochastically, i.e. they produce a different graph each time. For instance sample_grg:

graph1 <- sample_grg(100, 0.2)

This generates a geometric random graph: n points are chosen randomly and uniformly inside the unit square and pairs of points closer to each other than a predefined distance d are connected by an edge. If you generate GRGs with the same parameters, they will be different:

graph2 <- sample_grg(100, 0.2)
identical_graphs(graph1, graph2)

A slightly looser way to check if the graphs are equivalent is via isomorphic. Two graphs are said to be isomorphic if they have the same number of components (vertices and edges) and maintain a one-to-one correspondence between vertices and edges, i.e., they are connected in the same way.

isomorphic(graph1, graph2)

Checking for isomorphism can take a while for large graphs (in this case, the answer can quickly be given by checking the degree sequence of the two graphs). identical_graph is a stricter criterion than isomorphic: the two graphs must have the same list of vertices and edges, in exactly the same order, with same directedness, and the two graphs must also have identical graph, vertex and edge attributes.

Setting and retrieving attributes

In addition to IDs, vertex and edges can have attributes such as a name, coordinates for plotting, metadata, and weights. The graph itself can have such attributes too (e.g. a name, which will show in summary). In a sense, every graph, vertex and edge can be used as an R namespace to store and retrieve these attributes.

To demonstrate the use of attributes, let us create a simple social network:

g <- make_graph(~ Alice-Bob:Claire:Frank, Claire-Alice:Dennis:Frank:Esther,
                George-Dennis:Frank, Dennis-Esther)

Each vertex represents a person, so we want to store ages, genders and types of connection between two people (is_formal refers to whether a connection between one person or another is formal or informal, i.e. colleagues or friends). The \$ operator is a shortcut to get and set graph attributes. It is shorter and just as readable as graph_attr and set_graph_attr.

V(g)$age <- c(25, 31, 18, 23, 47, 22, 50) 
V(g)$gender <- c("f", "m", "f", "m", "m", "f", "m")

V and E are the standard way to obtain a sequence of all vertices and edges, respectively. This assigns an attribute to all vertices/edges at once. Another way to generate our social network is with the use of set_vertex_attr and set_edge_attr and the operator %\>%:

g <- make_graph(~ Alice-Bob:Claire:Frank, Claire-Alice:Dennis:Frank:Esther,
                George-Dennis:Frank, Dennis-Esther) %>%
  set_vertex_attr("age", value = c(25, 31, 18, 23, 47, 22, 50)) %>%
  set_vertex_attr("gender", value = c("f", "m", "f", "m", "m", "f", "m")) %>%
  set_edge_attr("is_formal", value = c(FALSE, FALSE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, FALSE))

To assign or modify an attribute for a single vertex/edge:

E(g)$is_formal[1] <- TRUE

Attribute values can be set to any R object, but note that storing the graph in some file formats might result in the loss of complex attribute values. Vertices, edges and the graph itself can all be used to set attributes, e.g. to add a date to the graph:

g$date <- c("2022-02-11")
graph_attr(g, "date")

To retrieve attributes, you can also use graph_attr, vertex_attr, and edge_attr. To find the ID of a vertex you can use the function match:

match(c("George"), V(g)$name)

To assign attributes to a subset of vertices or edges, you can use:

V(g)$name[1:3] <- c("Alejandra", "Bruno", "Carmina")

To delete attributes:

g <- delete_vertex_attr(g, "gender")

If you want to save a graph in R with all the attributes use the R's standard function dput function and retrieve it later with dget. You can also just save the R workspace and restore it later.

Structural properties of graphs

igraph provides a large set of functions to calculate various structural properties of graphs. It is beyond the scope of this tutorial to document all of them, hence this section will only introduce a few of them for illustrative purposes. We will work on the small social network constructed in the previous section.

Perhaps the simplest property one can think of is the degree. The degree of a vertex equals the number of edges adjacent to it. In case of directed networks, we can also define in-degree (the number of edges pointing towards the vertex) and out-degree (the number of edges originating from the vertex). igraph is able to calculate all of them using a simple syntax:


If the graph was directed, we would have been able to calculate the in- and out-degrees separately using degree(mode="in") and degree(mode="out"). You can also pass a single vertex ID or a list of vertex IDs to degree if you want to calculate the degrees for only a subset of vertices:

degree(g, 7)
degree(g, v=c(3,4,5))

Most functions that accept vertex IDs also accept vertex names (i.e. the values of the name vertex attribute) as long as the names are unique:

degree(g, v=c("Carmina", "Frank", "Dennis"))

It also works for single vertices:

degree(g, "Bruno")

A similar syntax is used for most of the structural properties igraph can calculate. For vertex properties, the functions accept a vertex ID, a vertex name, or a list of vertex IDs or names (and if they are omitted, the default is the set of all vertices). For edge properties, the functions accept a single edge ID or a list of edge IDs.

NOTE: For some measures, it does not make sense to calculate them only for a few vertices or edges instead of the whole graph, as it would take the same time anyway. In this case, the functions won't accept vertex or edge IDs, but you can still restrict the resulting list later using standard operations. One such example is eigenvector centrality (evcent()).

Besides degree, igraph includes built-in routines to calculate many other centrality properties, including vertex and edge betweenness (edge_betweenness) or Google's PageRank (page_rank) just to name a few. Here we just illustrate edge betweenness:


Now we can also figure out which connections have the highest betweenness centrality:

ebs <- edge_betweenness(g)
as_edgelist(g)[ebs == max(ebs), ]

Querying vertices and edges based on attributes

Selecting vertices

Imagine that in a given social network, you want to find out who has the largest degree. You can do that with the tools presented so far and the which.max function:


Another example would be to select only vertices that have only odd IDs but not even ones, using the V function:

graph <- graph.full(n=10)
only_odd_vertices <- which(V(graph)%%2==1)

Of course, it is possible to select vertices or edges by positional indices:

seq <- V(graph)[2, 3, 7]
seq <- seq[1, 3]    # filtering an existing vertex set

Selecting a vertex that does not exist results in an error:

seq <- V(graph)[2, 3, 7, "foo", 3.5]
## Error in simple_vs_index(x, ii, na_ok) : Unknown vertex selected

Attribute names can also be used as-is within the indexing brackets of V() and E(). This can be combined with R's ability to use boolean vectors for indexing to obtain very concise and readable expressions to retrieve a subset of the vertex or edge set of a graph. For instance, the following command gives you the names of the individuals younger than 30 years in our social network:

V(g)[age < 30]$name

Of course, < is not the only boolean operator that can be used for this. Other possibilities include the following:

| Operator | Meaning | |---------------------------|-----------------------------------------------------------------| | == | The attribute/property value must be equal to | | != | The attribute/property value must not be equal to | | < | The attribute/property value must be less than | | <= | The attribute/property value must be less than or equal to | | > | The attribute/property value must be greater than | | >= | The attribute/property value must be greater than or equal to | | %in% | The attribute/property value must be included in |

You can also create a "not in" operator from %in% using the Negate function:

`%notin%` <- Negate(`%in%`)

If an attribute has the same name as an igraph function, you should be careful as the syntax can become a little confusing. For instance, if there is an attribute named degree that represents the grades of an exam for each person, that should not be confused with the igraph function that computes the degrees of vertices in a network sense:

V(g)$degree <- c("A", "B", "B+", "A+", "C", "A", "B")
V(g)$degree[degree(g) == 3]
V(g)$name[degree(g) == 3]

Selecting edges

Edges can be selected based on attributes just like vertices. As mentioned above, the standard way to get edges is E. Moreover, there are a few special structural properties for selecting edges.

Using .from allows you to filter the edge sequence based on the source vertices of the edges. E.g., to select all the edges originating from Carmina (who has vertex index 3):


Of course it also works with vertex names:


Using .to filters edge sequences based on the target vertices. This is different from .from if the graph is directed, while it gives the same answer for undirected graphs. Using .inc selects only those edges that are incident on a single vertex or at least one of the vertices, irrespectively of the edge directions.

The %--% operator can be used to select edges between specific groups of vertices, ignoring edge directions in directed graphs. For instance, the following expression selects all the edges between Carmina (vertex index 3), Dennis (vertex index 5) and Esther (vertex index 6):

E(g) [ 3:5 %--% 5:6 ]

To make the %--% operator work with names, you can build string vectors containing the names and then use these vectors as operands. For instance, to select all the edges that connect men to women, we can do the following after re-adding the gender attribute that we deleted earlier:

V(g)$gender <- c("f", "m", "f", "m", "m", "f", "m")
men <- V(g)[gender == "m"]$name
women <- V(g)[gender == "f"]$name
E(g)[men %--% women]

Treating a graph as an adjacency matrix

The adjacency matrix is another way to represent a graph. In an adjacency matrix, rows and columns are labeled by graph vertices, and the elements of the matrix indicate the number of edges between vertices i and j. The adjacency matrix for the example graph is:


For example, Carmina (1, 0, 0, 1, 1, 1, 0) is directly connected to Alejandra (who has vertex index 1), Frank (index 4), Dennis (index 5) and Esther (index 6), but not to Bruno (index 2) or to George (index 7).

Layouts and plotting

A graph is an abstract mathematical object without a specific representation in 2D, 3D or any other geometric space. This means that whenever we want to visualise a graph, we have to find a mapping from vertices to coordinates in two- or three-dimensional space first, preferably in a way that is useful and/or pleasing for the eye. A separate branch of graph theory, namely graph drawing, tries to solve this problem via several graph layout algorithms. igraph implements quite a few layout algorithms and is also able to draw them onto the screen or to any output format that R itself supports.

Layout algorithms

The layout functions in igraph always start with layout. The following table summarises them:

| Method name | Algorithm description | |----------------------|-----------------------------------------------------------------------------------| | layout_randomly | Places the vertices completely randomly | | layout_in_circle | Deterministic layout that places the vertices on a circle | | layout_on_sphere | Deterministic layout that places the vertices evenly on the surface of a sphere | | layout_with_drl | The Drl (Distributed Recursive Layout) algorithm for large graphs | | layout_with_fr | Fruchterman-Reingold force-directed algorithm | | layout_with_kk | Kamada-Kawai force-directed algorithm | | layout_with_lgl | The LGL (Large Graph Layout) algorithm for large graphs | | layout_as_tree | Reingold-Tilford tree layout, useful for (almost) tree-like graphs | | layout_nicely | Layout algorithm that automatically picks one of the other algorithms based on certain properties of the graph |

Layout algorithms can be called directly with a graph as its first argument. They will return a matrix with two columns and as many rows as the number of vertices in the graph; each row will correspond to the position of a single vertex, ordered by vertex IDs. Some algorithms have a 3D variant; in this case they return three columns instead of 2.

layout <- layout_with_kk(g)

Some layout algorithms take additional arguments; e.g., when laying out a graph as a tree, it might make sense to specify which vertex is to be placed at the root of the layout:

layout <- layout_as_tree(g, root = 2)

Drawing a graph using a layout

We can plot our imaginary social network with the Kamada-Kawai layout algorithm as follows:

layout <- layout_with_kk(g)
plot(g, layout = layout, main = "Social network with the Kamada-Kawai layout algorithm")

This should open a new window showing a visual representation of the network. Remember that the exact placement of nodes may be different on your machine since the layout is not deterministic.

The layout argument also accepts functions; in this case, the function will be called with the graph as its first argument. This makes it possible to just pass the name of a layout function directly, without creating a layout variable:

plot(g, layout = layout_with_fr,
     main = "Social network with the Fruchterman-Reingold layout algorithm")

To improve the visuals, a trivial addition would be to color the vertices according to the gender. We should also try to place the labels slightly outside the vertices to improve readability:

V(g)$color <- ifelse(V(g)$gender == "m", "yellow", "red")
plot(g, layout = layout, vertex.label.dist = 3.5,
     main = "Social network - with genders as colors")

You can also treat the gender attribute as a factor and provide the colors with an argument to plot(), which takes precedence over the color vertex attribute. Colors will be assigned automatically to levels of a factor:

plot(g, layout=layout, vertex.label.dist=3.5, vertex.color=as.factor(V(g)$gender))

As seen above with the vertex.color argument, you can specify visual properties as arguments to plot instead of using vertex or edge attributes. The following plot shows the formal ties with thick lines while informal ones with thin lines:

plot(g, layout=layout, vertex.label.dist=3.5, vertex.size=20,
     vertex.color=ifelse(V(g)$gender == "m", "yellow", "red"),
     edge.width=ifelse(E(g)$is_formal, 5, 1))

This latter approach is preferred if you want to keep the properties of the visual representation of your graph separate from the graph itself.

In summary, there are special vertex and edge properties that correspond to the visual representation of the graph. These attributes override the default settings of igraph (i.e color, weight, name, shape,layout,etc.). The following two tables summarise the most frequently used visual attributes for vertices and edges, respectively:

Vertex attributes controlling graph plots

| Attribute name | Keyword argument | Purpose | |----------------------|----------------------|-----------------------------| | color | vertex.color | Color of the vertex | | label | vertex.label | Label of the vertex. They will be converted to character. Specify NA to omit vertex labels. The default vertex labels are the vertex ids. | | label.cex | vertex.label.cex | Font size of the vertex label, interpreted as a multiplicative factor, similarly to R's text function | | label.color | vertex.label.color | Color of the vertex label | | label.degree | vertex.label.degree | It defines the position of the vertex labels, relative to the center of the vertices. It is interpreted as an angle in radian, zero means 'to the right', and 'pi' means to the left, up is -pi/2 and down is pi/2. The default value is -pi/4 | | label.dist | vertex.label.dist | Distance of the vertex label from the vertex itself, relative to the vertex size | | label.family | vertex.label.family | Font family of the vertex, similarly to R's text function | | label.font | vertex.label.font | Font within the font family of the vertex, similarly to R's text function | | shape | vertex.shape | The shape of the vertex, currently "circle", "square", "csquare", "rectangle", "crectangle", "vrectangle", "pie" (see vertex.shape.pie), 'sphere', and "none" are supported, and only by the plot.igraph command. | | size | vertex.size | The size of the vertex, a numeric scalar or vector, in the latter case each vertex sizes may differ |

Edge attributes controlling graph plots

| Attribute name | Keyword argument | Purpose | |-------------------------|-----------------------------|------------------| | color | edge.color | Color of the edge | | curved | edge.curved | A numeric value specifies the curvature of the edge; zero curvature means straight edges, negative values means the edge bends clockwise, positive values the opposite. TRUE means curvature 0.5, FALSE means curvature zero | | arrow.size | edge.arrow.size | Currently this is a constant, so it is the same for every edge. If a vector is submitted then only the first element is used, ie. if this is taken from an edge attribute then only the attribute of the first edge is used for all arrows. | | arrow.width | edge.arrow.width | The width of the arrows. Currently this is a constant, so it is the same for every edge | | width | edge.width | Width of the edge in pixels | | label | edge.label | If specified, it adds a label to the edge. | | label.cex | edge.label.cex | Font size of the edge label, interpreted as a multiplicative factor, similarly to R's text function | | label.color | edge.label.color | Color of the edge label | | label.family | edge.label.family | Font family of the edge, similarly to R's text function | | label.font | edge.label.font | Font within the font family of the edge, similarly to R's text function |

Generic arguments of plot()

These settings can be specified as arguments to the plot function to control the overall appearance of the plot.

| Keyword argument | Purpose | |--------------------------------|----------------------------------------| | layout | The layout to be used. It can be an instance of Layout, a list of tuples containing X-Y coordinates, or the name of a layout algorithm. The default is auto, which selects a layout algorithm automatically based on the size and connectedness of the graph. | | margin | The amount of empty space below, over, at the left and right of the plot, it is a numeric vector of length four. |

igraph and the outside world

No graph module would be complete without some kind of import/export functionality that enables the package to communicate with external programs and toolkits. igraph is no exception: it provides functions to read the most common graph formats and to save graphs into files obeying these format specifications. The main functions for reading and writing from/to file are read_graph and write_graph, respectively. The following table summarises the formats igraph can read or write:

| Format | Short name | Read function | Write function | |------------------|------------------|------------------|------------------| | Adjacency list (a.k.a. LGL) | lgl | read_graph(file, format = c("lgl")) | write_graph(graph, file, format = c("lgl")) | | Adjacency matrix | adjacency | graph_from_adjacency_matrix(adjmatrix, mode = c("directed", "undirected", "max", "min", "upper","lower", "plus"), weighted = NULL, diag = TRUE, add.colnames = NULL, add.rownames = NA) | as.matrix(graph, "adjacency") | | DIMACS | dimacs | read_graph(file, format = c("dimacs")) | write_graph(graph, file, format = c("dimacs")) | | Edge list | edgelist | read_graph(file, format = c("edgelist")) | write_graph(graph, file, format = c("edgelist")) | | GraphViz | dot | not supported yet | write_graph(graph, file, formati = c("dot")) | | GML | gml | read_graph(file, format = c("gml")) | write_graph(graph, file, format = c("gml")) | | GraphML | graphml | read_graph(file, format = c("graphml")) | write_graph(graph, file, format = c("graphml")) | | LEDA | leda | not supported yet | write_graph(graph, file, format = c("leda")) | | Labeled edgelist (a.k.a. NCOL) | ncol | read_graph(file, format = c("ncol")) | write_graph(graph, file, format = c("ncol")) | | Pajek format | pajek | read_graph(file, format = c("pajek")) | write_graph(graph, file, format = c("pajek")) |

NOTE: Each file format has its own limitations. For instance, not all of them can store attributes. Your best bet is probably GraphML or GML if you want to save igraph graphs in a format that can be read from an external package and you want to preserve numeric and string attributes. Edge list and NCOL is also fine if you don't have attributes (NCOL supports vertex names and edge weights, though).

Where to go next

This tutorial is a brief introduction to igraph in R. We sincerely hope you enjoyed reading it and that it will be useful for your own network analyses.

For a detailed description of specific functions, see https://r.igraph.org/reference/. For questions on how to use igraph, please visit our Forum. To report a bug, open a Github issue. Please do not ask usage questions on Github directly as it's meant for developers rather than users.

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igraph documentation built on Aug. 10, 2023, 9:08 a.m.