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A control-flow graph (CFG) is a directed graph that shows the possible paths execution can take through a function or procedure. Its nodes are basic blocks—straight-line sequences of actions—and its arrows show the possible transfers of control from one block to another.
What are the nodes in a control-flow graph?
Each node represents a basic block: a sequence of instructions or statements that executes in order, without branching into or out of the middle. A block has one entry and one exit; the instruction or action at its end determines what can happen next. LLVM describes a basic block as a single-entry, single-exit section ending in a terminator instruction (LLVM Programmer’s Manual).
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Within a block, statement order captures unconditional flow. In a source-level Clang CFG, for example, statements appear in order inside blocks, while conditional control flow is represented by edges between blocks (Clang CFE Internals Manual).
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What do the edges represent?
A directed edge indicates a possible transfer from the end of one block to the beginning of another. If a block ends with a conditional branch, it can have multiple outgoing edges—one for each possible successor. The terminator must select which successor execution takes. Edges can also point back to an earlier block, representing a loop.
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The graph describes possible control transfers, not a guarantee that every edge will be followed in a particular run. LLVM Flang defines a CFG as basic blocks connected by directed edges for possible transitions, including transitions from a block to itself (LLVM Flang: Control Flow Graph).
How do branches and loops appear in a CFG?
Branch
Suppose a function tests a condition and then either performs one action or another. The test ends its block with a decision, and two outgoing edges lead to the alternative blocks. Those paths may later join at a block that follows either outcome.
Loop
A loop is shown by an edge that returns to an earlier block, such as the block that checks a loop condition. The return edge represents another possible iteration; a separate edge can lead out of the loop when its condition is no longer satisfied.
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One free scan finds every outdated or missing driver and matches the right update for your exact hardware.Free scan · exact hardware matchThese are structural possibilities. A CFG alone does not say how often a loop runs or prove which branch is taken for a particular input.
How do compilers use control-flow graphs?
CFGs give compilers and other program-analysis tools a structure for reasoning about what might execute next. Clang notes that CFGs support flow-sensitive and path-sensitive analysis. A data-flow analysis can propagate facts—such as information about possible values—along graph edges and repeat the calculation until it reaches a fixed point, where another pass produces no change (Clang: Data Flow Analysis: An Informal Introduction).
At a branch, an analysis can track facts along each possible path; where paths rejoin, it can combine the information from those paths. This makes the CFG useful for analyses that need to account for execution order and alternative routes through a function.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Do all CFGs have explicit entry and exit nodes?
No. Entry and exit blocks are conventions used by particular representations, not a requirement of every CFG. Clang’s function CFG includes special empty entry and exit blocks: the entry has no incoming edges, and the exit has no outgoing edges (Clang CFE Internals Manual). Other graph forms may handle these boundaries differently.
Language features can also affect a graph’s entry structure. LLVM Flang notes that a Fortran subprogram may have multiple entry points through the ENTRY statement (LLVM Flang: Control Flow Graph). So when inspecting a CFG, check whether it represents source code or an intermediate representation and how that representation handles entry points, exits, and language-specific transfers.
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In one sentence
A control-flow graph models a function’s possible execution paths as directed connections between basic blocks, with each block’s terminator determining which successor or successors are possible.
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