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vertex is its outdegree (called branching factor in trees). Let G = (V, E) and v ∈ V. The indegree of v is denoted deg−(v) and its outdegree is denoted deg+(v)...

Laplacian matrix is singular). For directed graphs, either the indegree or outdegree might be used, depending on the application, as in the following example:...

theory, the branching factor is the number of children at each node, the outdegree. If this value is not uniform, an average branching factor can be calculated...

if every vertex has outdegree at most 1. A functional graph is a special case of a pseudoforest in which every vertex has outdegree exactly 1. By Brooks'...

vertex with degree one. In a directed graph, one can distinguish the outdegree (number of outgoing edges), denoted 𝛿 +(v), from the indegree (number...

leads to an outdegree- k {\displaystyle k} orientation (by choosing an outdegree-1 orientation for each pseudoforest), so the minimum outdegree of such an...

number of arcs incident from (respectively, to) a vertex v is called the outdegree (respectively, indegree) of v and is denoted by od(v) (respectively, id(v))...

graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. A regular graph with...

of the graph and K {\displaystyle K} is the diagonal matrix with the outdegrees in the diagonal. The probability calculation is made for each page at...

v i {\displaystyle v_{i}} has indegree a i {\displaystyle a_{i}} and outdegree b i {\displaystyle b_{i}} . The problem belongs to the complexity class...

methods. If every player beats the same number of other players (indegree − outdegree = 0) the tournament is called regular. The number of unlabeled regular...

Often trees have a fixed (more properly, bounded) branching factor (outdegree), particularly always having two child nodes (possibly empty, hence at...

ultrapeer is connected to more than 32 other ultrapeers. With this higher outdegree, the maximum number of hops a query can travel was lowered to 4. Leaves...

n ) ) {\displaystyle ((a_{1},b_{1}),...,(a_{n},b_{n}))} the indegree-outdegree pairs of a labeled directed graph with at most one loop per vertex? The...

centrality, namely indegree and outdegree. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that...

each edge of G such that, at each vertex v, the indegree of v equals the outdegree of v. Such an orientation exists for any undirected graph in which every...

Internet service and infrastructure, assigned AS701, maintained the highest outdegree of any ISP.[clarification needed] In 2006, WorldCom was purchased by Verizon...

computer-supported collaborative learning such as: density, centrality, indegree, outdegree, and sociogram. Density refers to the "connections" between participants...

has indegree and outdegree equal to n − 2 {\displaystyle n-2} , while the central vertex in P {\displaystyle P} has larger outdegree n − 1 {\displaystyle...

graphs of maximum degree three, directed planar graphs with indegree and outdegree at most two, bridgeless undirected planar 3-regular bipartite graphs,...

e1 and e2, connecting to a new vertex w of degree-2, or indegree-1 and outdegree-1 for the directed edge: Determining whether for graphs G and H, H is...

graph in which each vertex has at most one outgoing edge; that is, it has outdegree at most one. A directed 1-forest – most commonly called a functional graph...

product gate. An arithmetic formula is a circuit in which every gate has outdegree one (and so the underlying graph is a directed tree). A circuit has two...

refer either to indegree (the number of incoming edges at each vertex) or outdegree (the number of outgoing edges at each vertex). The following undirected...

exhibits the following additional properties: all 0-indegree and all 0-outdegree vertices appear on the same face (often assumed to be the outer face)...

Eulerian circuit if and only if G is connected and the indegree is equal to outdegree at every vertex. In this case G is called Eulerian. We denote the indegree...

{\displaystyle ((a_{1},b_{1}),\ldots ,(a_{n},b_{n}))} to be the indegree-outdegree pairs of a simple directed graph; a sequence obeying these conditions...

structures, and game theory, the number of children at each node, the outdegree. If this value is not uniform, an average branching factor can be calculated...

by distinct symbols of the alphabet, both KUM and SMM graphs have O(1) outdegree. However, KUM pointers' invertibility restricts the in-degree to O(1)...

decision problem is NP-complete, even for sparse digraphs of maximum outdegree at most 2. On the positive side, the problem is solvable in time O ( 1...

{\displaystyle D} of G {\displaystyle G} such that every point has indegree and outdegree = k {\displaystyle =k} . Next, replace every vertex v ∈ V ( D ) {\displaystyle...

directed graph with the symbols of a k-letter input alphabet (where k is the outdegree of each vertex) in order to form a synchronizable DFA. It was conjectured...

across the entire CFG, every edge A→B should have the property that: outdegree(A) > 1 or indegree(B) > 1 (or both). Such a graph can be derived from...

v is an acyclic subgraph of G in which every vertex other than v has outdegree 1. This definition is only satisfied when the "branches" of T point towards...

are pairs of non-negative integers ((a1,b1), ..., (an,bn)) the indegree-outdegree pairs of a labeled directed graph with at most one loop per vertex? Similar...

every two vertices u and v, either there is an edge from u to v or the outdegree of u plus the indegree of v equals or exceeds the number of vertices in...

is then a directed path where all internal vertices have indegree and outdegree equal to 1. A directed graph is strongly connected if it contains a directed...

with fewer traces, improving accuracy and analyzing POP sizes, router outdegree, and inter-domain peering. Assessing path inflation across 65 ISPs, he...

strongly connected directed graph in which all vertices have the same outdegree has a synchronizable edge coloring if and only if it is aperiodic. Jarvis...

even with strong restrictions on the graph, such as small indegree and outdegree. Furthermore, even finding an ε {\displaystyle \varepsilon } -approximate...

of arcs enter i {\displaystyle i} , d i + {\displaystyle d_{i}^{+}} (outdegree) is the number of arcs leaving i {\textstyle i} , and d i {\displaystyle...

+ 1 {\displaystyle x+b\in V_{i+1}} by definition, so every vertex has outdegree equal to the size of B {\displaystyle B} .) Then G {\displaystyle G} is...

graph (an orientation for which every vertex has indegree equal to its outdegree) may be found by orienting the edges consistently around the tour. These...

defined as two separate measures of degree centrality, namely indegree and outdegree. Betweenness centrality quantifies the number of times a vertex acts as...

directed graph, is a vertex of indegree n − 1 {\displaystyle n-1} and outdegree zero. The existence of a sink can be tested with less than 3 n {\displaystyle...

it is often assumed that all nodes have strictly positive indegree and outdegree: again, the theory of graph (op)fibrations can be developed without such...

vertices and 126 pairwise arc-disjoint 4-cycles with regular indegree and outdegree 3 and no circuits of lengths 2 and 3 by altering a definition of the Coxeter...