We explore the characteristics of the cosmic web around Local Group ( LG ) like pairs using a cosmological simulation in the \Lambda CDM cosmology .
We use the Hessian of the gravitational potential to classify regions on scales of \sim 2 Mpc as a peak , sheet , filament or void .
The sample of LG counterparts is represented by two samples of halo pairs .
The first is a general sample composed by pairs with similar masses and isolation criteria as observed for the LG .
The second is a subset with additional observed kinematic constraints such as relative pair velocity and separation .
We find that the pairs in the LG sample with all constraints are : ( i ) Preferentially located in filaments and sheets , ( ii ) Located in in a narrow range of local overdensity 0 < \delta < 2 , web ellipticity 0.1 < e < 1.0 and prolateness -0.4 < p < 0.4 .
( iii ) Strongly aligned with the cosmic web .
The alignments are such that the pair orbital angular momentum tends to be perpendicular to the smallest tidal eigenvector , \hat { e } _ { 3 } , which lies along the filament direction or the sheet plane .
A stronger alignment is present for the vector linking the two halos with the vector \hat { e } _ { 3 } .
Additionally , we fail to find a strong correlation of the spin of each halo in the pair with the cosmic web .
All these trends are expected to a great extent from the selection on the LG total mass on the general sample .
Applied to the observed LG , there is a potential conflict between the alignments of the different planes of satellites and the numerical evidence for satellite accretion along filaments ; the direction defined by \hat { e } _ { 3 } .
This highlights the relevance of achieving a precise characterization of the place of the LG in the cosmic web in the cosmological context provided by \Lambda CDM .